SlideShare a Scribd company logo
1 of 104
Download to read offline
,2
-mEegx
l
rfere&ev
@ ln/r'.rte doum o- mob,i< in lla gala:."1 b.t n .
Ed; t
"t
L6 con4;dat, o- ze.t 9b inutloi,zoqa -
eq,"ttipn ,
t +2y +32 15t -o
+L -rzy+gz+7* i o
!t- +4y +u2 a g2 , 6
Now, we wlile down Lh.e
otr jt"4 d.6aveeL,,.tiory
"::::;f;;: ^11;.,br"akel^ qrd. lhzn wq Be*"
n=f t 2 z E1
l+ z i ''
Lt i 2 il
12, ab'1e sy,tern o,l- ,rarnbeyA - anq1gpd ) n a"-retto.n}l/an ),rl,owt qtt| eolum,t and. bo4la{ ty
Lh-z brqehel,,, jj, callpd- + no7-rt.
An mo,l."ix b Wz"l m.^ ,_r"*.n
^,
t%,"L,tt-
^-ly't:
!.9!^yt:2) Any 1xn ^,nalr),twt;< hot
o y orL. -+ -r.ow qYld n eoju-m'v, ). e
"A-al
R+ row n"inir .
L6-.j a, . ,.. . arj
Et A=lJ t zl
-t /n
_Lt3
_. COtirm.r -tn<,,trtxI A..!------'----^!,--'^
ftny 'nLtmbeY' o,k t:ov,tx
Et , A,.l t]
. l:l. ,3xL
3 Or-thca-or.a{
-Jri
xI 4
-,-t_^,1^
ar a'.lhcyona T^o'Lr"'
/l crr J. t]1 )-r"r'tlozz
rlr oJ-.irz
A,A,..
'"8wt=a
-"aL'r,,t h0, l' + oqe q4lwn a .:, 1d
p eolk d q col-,,-, ).Ltr..
-r.rqqre tq-trl,< A "tr, t-Wa"
,6 )4P prci,J ob o, ,",, ,
t1otr)x A' it on. ilzrl;"ty
+. !,rof e l",Jrir ;
.-;=^-T-_noWA 2A eq-i{o,
-gctko.ne Toopt( ,
A 'no,tli
r. in wlrrch f,hz number o1-
o&
Al .'n 11
r- otri r-,
F-N,'. A -
!o Lhr nu-ben sb " Iurntv5 i,. '",/14d
^ra
"*r, re
T. 3f
ul ro3
w }.iel" ra = r A <Jizd zaat<
9-rne,y
b) l2
y,$3{t{i -Iwo vnol-pk<zv,a're .',d'd t'a be
:l
RXtJ{g< 1l'z- rn,1n mqTot ^Jho;,eekt "t.tzole o.l-{ 2<Ta iL cquLd_ L.e nu!_I.-DJ'nt",
F't'.
x=1'oo1
P ol_ ) 2.r,L
I
n."*-r"t Ynatnia:a ".,,^-...,.
- molr"r,c ,+
"rtWa
q- d;ayrnJ
t"oF., L . Lb o"U ,)
"."
. tW""^ eb,"ert' .ire 24 to
oR,,
%'fr"i- B,i
i*',
oit'e ok Ih4
el4n4L }i Lhr.
Adr,e oyd4r, ar oir,< ,tn I
corretpahdlA- por,ili*. ane
-5Xacr.enatr.ir )> cqu4d
L,r*o'dl el,sJw,.L a're +,.ly
6,i2 zef a ,
b"" r-.'.n[r z] B-,lL
trq p
A -cq"o'e -"j"'' A 'La,il
-
ho',2 elo.".zn)+ qDove anq
11,'i.,r*,0"'*^ e";",i *, a),!z<ro ; <altz^u^2.an lholr; <
t.: 4. [r o ] , St., ol
Lo*1,, LS L i|ur.,
8.Uni.t on Sd{nl"ly
-olni,.
i A
r--,----^--_-----l- _
-
a utrrt )"n#'.ir. $ oll ult
o.nL -no, &a3""""1 elZrufrA
bbk,
A dl'cX^orar
colta.{ o.n
-o;.i1l
d,ia;,ona.l
idan*,i.*>n"ir'x '
e.!zr"xrt^ q-rg o)1 onz i+
Et"
9. Sca-(el .',aLt'* i
Z--!2-'-'-2------2-'.!
a:pe aU e.y Lcul-b
Lt- . A = | eL
La
h d:"go-"l
al1z.d a,
,"olfix k"1p"J
-gcqlqr, zo.*rjz.
Ir o o1
A-,lo 7 o I
ln o 1 |
L" -)
ilrrr
oJ1 trpper it)en4llla 'h;LY))'
pr;n<rp"-[ &ayanJ dr e 24-ro .
A=lt z v-l
lo z t 1
loo +l
" ^3^3
eter.ab,
-5xq^re;
.r,J''i,,L ,9--Lo-;;7
& tlra d4nain L<lavti^
f},r'
Et-,
LL L'o'.Ler/:t)n,gaar toty.ix : A >tTo.qie n at.'",t A =
W*
a& *hP el4i'''znt'
lt z ptit dpo! d'aynJ ate z-zt"<>
aool
LTal
3 4 +)txs
C qJ O y4rr-'tu ' r. ps Qruh4]? t f Yia-,ti
. , ..ll
tz .ASym 'rnetT.i' mN 't , A )'4u e maLI) * """-
a Q{16:,ymnoltj c..Det€rnih-}e ar vxli | : be c&lPA
81,. A
-
/a- -l
4bove
/- --------',-'1--an ^'n"i,JX -+ -b"--"ij -v tr"' a)' i at'f, 1 a,
i
0t, k'= A '
lr
wfPQY
7 aR,
A
^Iaqve
--^L-ti/'h+A=s-L"ri A Aqtd i.o E<6e
-:r-y:,". t
.ij- ( ,. i), cle
-_
nt i* tiz +an<
l,
^r,.,t el,evvalgs.s,,
"l ,, ..or, bT o-14
Et' a,
Li Ske't sym-ujri< :"no,l,-rix'A >r+,+re ,natt; * t+ , nAted
/..-''----....-/-'--"....--^-^
9l1ew-.symp2trie To|aix , )L
,) nri- . nj; |,"r Jl "Ltue;
.E 1 &4 ot A'- - A
h) Atl.l,qo"*|" o-lzn"znl.^, a."<. z,1.,vo.
OR
ah3,1
h b,f
/
9 { cl
i :1",[r o o 1
ln 6u I
lzi+ |
L 'Jt'9
L.-f.
u.a.
t!,Sit'.X."ctor "-
q,tri'. I
,'!--!-^'^-,.
'fo,.tirb< j* 24ra '4'14:n
:ltng:tbv 'r" otatt< At'
g"r 1Al =l L 2J
' L3 4)zrt
LC,I'qpo6z ob 'motr'r,, i q*
/./.-'J.-.'.---'',,.
ll,terrhon;< *l'e row,s qd *U
3|. *hz dal€th)h an* ok :LM
lv"e. n*bi x "b l,nown )a
,tb
L-L --o l:he].^h b' a Sing"J*
roJr.4-t,
L ttv<h
'-.^|]i.)< A, 4Q
ea'fie, pordjrly eo,l.Qr,n4
xhz- 'Mw
a)'- khz
t-'atr)t .L.E^nzd ) c
^.!-trpd,
fW:- *vatapaqe
'(naf.rr t , i/.
^
d4ndte| by At , b
or<.
ue,
A,
F-*|
A --lurjl
-^n
th-eu "tV L11r ^ma*tix aLlivd
A by evung.iny*s tart ;t;fo columa an)
colu',tt4 )lnto ttt z i* ."U'zd *hz l."apo""< o,E
t
3
,', A' or' A1 --
17. Uni1".ry r)o"tr)t ', 4
/'_---'^------ A ,,,t -.ta'd
tp b€. |.tll*o.Py- ,l Ae4
^[:
lr . e1
l3
o 7 |
| + 5 3l
L 's'=
j
o
7
.tr<Lu!.r'e
=fi.L"
i,
-:I
l
-l-j
-t
L+'
oli o 1loytna)
A qnl 1i€
tl. aR*ho2r:na.!"
+.-rtaUpaS.e ,1aL"-L/
',^t-it ,jtr:
". AA'- Ata --I
JLr tAt:
) ; "-,oJtt t- AL ?rop?P
Lt. Ccr:lcratz ah- tno,t:.ix .. LJ
"-.,-----' -.- -.-/-/_
^
0 | (. c
^t]_e
ot ca^7ag^Jer, a ot
-aF
^h..L
atz-r. cL
'
-L: a +iri
{rnDte4 b t j-;';r
< La bt
^
L
oF 'mo'trit"
Erarpk, W.,
^-1,
car,i4FJ:z o.I, tJnx fiA F
-1
I
Lhz
'rYrdLrrtrL
A
Pl,odLlcl, a,E
a c a.!,lzd
),,
"1:.1y
r,rrte.r '1 i, )zf .:,^lI 1",?n 7, q1-j
t eo,npi,ott number . -6* cc,mplax :"omi<-rn o-+6i and c_6j,
o- alrd b re-{
I'un, tU", cor)4qyatc
*d ;b, """iul. )
. ).t1,t c..lkd cagwg^t<
:,,1
:,,1l].;,
ZCt.Hez,r.tl:;a.n ^n,*r)x :
--__----__,-
rl =la^rl .ruc t"1
A h HaFm&q.,
-$gL{are
r,d-tr-t>c
4 6 <"J!<{
A
;, Her"r"";;L
valuz4
",& i and l',
DA ar 9i€*- ha.nrnitiqvr
p l,
A tl,tare lna*i tc 4
h4r o.l-i,tj
"", -^"1.111 ,)y
a. - : a. hot' o-!)
a7 At
rth2 k,.yon"- elzraaala
q).e. reo-t nqmber).
cotl,lt tz
?ro dzd
Ci-zar)"
OR,
,4 *q.u."a r1;lr; t A.lct,)) La e
^!!zd
h4".j-fur'.
-J,it
i, Qve?y- ',-i t e!,,n"^J ab n i^, ey"! b (a.j,a4e
ap^pbr'. 4- i th oE 4 ,
9t,otlt v a.p!)-*,, __u-,ltiti;
t;_,,
:.: r
N..tgo,y ", d- ...tt.o-
^}1 ""^*L1ti)Ait'" t:'J,, ",
1e 6e Het'niLiqn -i) ,{-qJ 4 , oU on
Xr^Apo),< o,e. 4,
4"-U)'
2L 9kew - l,,zom)j)qo mol'nix l -tLu"qi<
-.,q|.
t |._LiL,,
A
Aqe *rot. At - - ft t colkd *kew, hq, hqn . -hc,-t
4 *
4vew' h.e:rmi'ti">tprovikL 6,;4
-..;
br col,XvJuzt
dr .L and- i. Cko'ty , th,z kq*ohd1 el<vznlt, o/- o,.
We.t - hzrh+k^t1 t,r_fi,.rz o^<
',to-(iN)c,
' Q)+t'n' -4ra-5 oY Ptrt'e
'. to,, ,
-
))) b< . ql.!r), o- 3fr r'))
<!-1y t_ 7 fl1 eb rrr,t b A 2
-I :_""-t tu w tul)uz e">,)ug^te ( ov'.,pb,La.!,
F t, '' +,, <Izr"<",h
"). /] .
i
"
o*rtan vrorl4: q,, =, t., 4j _ii
A lit
nL- itL4 .,1o,,u,+/t ,n ) vLe _".
o b t.Lt t. a. h .
r' uP'L d'oytnJ
^
LU
a-'-."i) - - q..i at, d.. + a. - d
-
an-qa,b
),*"
: d;..,= x
^b
.(cr+)b ) tLq ,b) _/)
;, Zq =o
a,.6 J pq'fe.
^-
agnqr.y O.t"
aU JaW &.aq1:lna.!.etznwlz
,ne- eLtzr za.jaa a.r pqr e,
*t
2- 3;
o
2;
5e
o
o- Atlea het ., tL
i^ajljt11)a
t"7 4z-4
9o
f{ovt
'lJ,.r
":?'l
-3t ,l '
A -+ucb
n
))1a
f;t^.
I ( Zr3^ 
t'
L- Lf-t) )
Lu 1dzmpot<tdt o:fu).*.
1-_/--__,--,__-- _.,'-_____-_
^
)o 6Wl, 9dtnpot"t*
".^ttOl{rEt'.
A,f , z -y1
/1 3 tl
lr -z -3 I
^-- lz -t +1
"-l: j +l
t' -L -3 I
=n
: .,1
2l -I''lcom-l .l.o,1f
{( . fi.z syi*q
/_.'/-_----- /=^
oA- nttynLer^
dT]c|x,€d-
-.i q t<6to1"olz{qr
eo^Lr-n, o'rA L.ullzd by
ro?Yhql ]^qtrix,
6
I
2*, 9nverl4,^ o.l- o_ :'t,-Lr) x I g,L- lr.to
.md: ee-t, A .,t dB/_-___--__,--- ___, ____, ___,_^
oa?e Lwo .>"6an'e, tn ql1.r.z^ o), th<
-XdnL4
ord!j,, Lrch
L,* g.ttt ra.i!-et *.V,2 )r,er4oz A cnd n A /h< vucta4
ol- B,
E/'. B-,A'r, whzte AB= BA=I,
2j s."uJop rno,Ir"4' 41- thc .td?t,,"vaal oE L*:- na|n. iz
zala, Lhak LLL nvLtit .i-', no".'1 ax -inytlar v,a.t t ,
E,(. I AI=IL 2f = L- e =a r l,a! 4
"z
a- ingul+, talr)c,er,,
13 el
.2f-Ncn- a,"ya!ao r"Je',r:9t J2 S2/z'tru-)e
..---_-----,.-{,-,-''r.----'.--^'-J,il
^io|
z-'e"co,*hzn ht'z'r"J 't -rz
q'fr1.dy )n ^Pou/^
'L
*h2 oro<he 4 ./Lt
qxd,
c".!tkA
i),,
Nayr,*"'r5.rl,tor -r,,J"iz .
rt'. lAl{a ,lhzn A A a- Na1- 44*utot hdtD tz).
non- in4oz
be i*;-> .
afun a 51r.ore-mati* n"t )nv
,^. -,-'--.-,-' ---^---------'ry
A snytat'< ''habiL" A' *o
Va4^/,A dn inver^z- j4 1r3 "n1*kix A A
, J)t ^ n" a o- 4nLL6re 1. d-ti/- a,, d. ,6g a
e'r// , kvu"' 4g -- I A: L ,
a?ro.e r...1r-ra
YncLLn)ce a$/ t)<
aE 4 an" 4 p
L"*
t /-/rrRrcEs
/ .
^
/*^^-
l;::*::"*:-*
noLo,n whzn a.
C
'4, -
<9L< , t- / qnqg o.ne l_o q,ope
::Ytz
otdeP
' Ntch LhoL, ae=u,-t
L^en B 42> c o-trlza 1^-e
f,z l,n,t<n* ok B a4 n =g) .n'eY+e
fi.ve4
lLr o ltore rnolp' /, 4 ,A rta.t- unNop
lfrl*o. i:se",
^tuq)"e.moirix
Ata poN4-eg
)'l e42
tg.3h A_lr -t 6l
" -
l" -t
" f t-0.o't Yzo"sl
Lt o ol
Lh'*,
,l=[r -1 o1
Jz -' o/
L7 a al
_x -1 o/
lL I al
,l
L.r a a-l
= I(o- o) + ) ta-
G)=o
dzt'LA)
o1- o 1c t-J)
' d?a
Co- ,F,',e.tot ok ArB
2
l
-l-a
o
a
a
L
lo
:l
A",
'L
a
'L
-f
-1.
La+J)
Io*J
(-r1 1
I"
. t1 o1l
a
t ol
:T
O
62-
l
l;,l-1
01
- l-r o
oO
o io-1*
q.-(o*)
lo , :'l
=
0
-b -t
I
lat sz | |
^/
' AqtA)=v') '-
:l
I
F,
1l
;l
[o o
- J
o-t
LL "L
i"". r+*+ LyB)l . grp, .whpnA o^dB arc
rarik kdJ mt M),p,tt,ol;on- oR_ no-.)-inq,.Jq h,rrirog
3b A o-rtd"B et"e. coraPqFohlz '"vtr;e,+ andA"
oqd B qlaA Lh,z tt'+Upo42 ma1 .z- o E A a nd B
,15-,r'
w hare
It
?;
be o.n
b< qn
mc-L t
AT
1;,4
)
ai)-12'
c. h.
Ye,V"tlive)y, ft,lzn pooveth"I, @{= n'B- Lza]
J), A md B qr< Lluz t-wo tJ ee+ eo,,b"vnA
y'6duxt nB, i: h'en ,1how *hJ (he) =s'a'
"a " v4 'oePre;"er1lz*oo4p4tn r a- ,nait')x -
/2
B-- b,,
9;,ntz, pB h *, *rp rnJ.r^r.
6a e1-
-t
a p xh tnotr) r .
6ur[htzr BT b gx.' moir)r. and
r-ol,rr)(. l-heretol
" , B,n,
^fruo
, (0a)' ond grsr
^rr""--';:Na-, {V 1-.1.;44 e.!2,,,,^t
de.,zrt, o,t: (nei _ i" ^
6
=
?'
o"
^oio
AXAa)
'fi.4
4,L T aa J,
c' 1,*hz i,t colr,,r
'r ah T X>.
"? /)o,1ae a?d?,
".-,bi,
tAB) -
Flg,ol'r @ ard @ ,we have (i,
d, UBf --U,i),Lr, <1Lzwzntdr
At, /hLz v o,tix LABf ,tnd B'Ar
A I de" o.rd .l M" (orret,lafla;4y c:!pr,.-_L
equ ol
9o, (/+B
ryg), 4 an
ve *ht
T /-tr_1
-v )
(nB) '
dBar.
|
^^
-lrHb)
-
B n
f Zoo;,)
13n-".
->'tnyt'-hr
r*,o (n'')
b-a-lk ;k
;) t',h elznzxt
Btnt,
qne tz A az.€
a>e
n^r) 1ea2) ,
-2
'4 AnA
erJ
'.4
t--
- i (AB)B-'I A-L^J
, t3fto'11n-r
'- (A,j).At
LBe-"-t
=L
)t-, B'n'-
fpro v
kno*
(nn,t
P1oo
fn')
9al' '
*hd'L
( B-ra-r )
te
ho,
B-LA
''(ns)= a-'yn-t1nesJ
-
B-'l(A*t+)Bf
=;r0,0
. B-'B
=1
Jd;,^k""
",&-L/nveLL<
o)-
Be'
- By Lhe
za6,ttrx,
B ' A-L
.i.t- ),
r* .)_ , s
,'' (ne;t: s-Lo-t
f PPoveeJ
-J
u)',4,
ah?re lA-'))-lrtt) .lP 4 {a co?cf
', t -lo) | suet,Jl^dni3=L
,- /
't:tar, 4= g-t
=t
i oe]_-q t_T
r.JocJ.
tr
Lr f aee) I
n') =H
' €..uq
-1
T_ / ^r )
Ler ,
(r
(0"
' I' - Loo--'f
t
= (A''')
',
n''
_Q.a,-,1-1. o-'
= (!--")'t . rt'.n '
=Q"')-''l!r'
- @'t 1)-',1!";
=@rt1-L,p-2t
=p-t;a'1.n-rz
-(n-11'7*z
| _) .-L
=U-)
. @')-'=1n'2.
lPro"eq
-lazorem ., Eveoy 2,;.1a"re
-n;L'rir-
can be,
/'<
^-/"-'-'-
€
it-aquzy e lpoeAAzd- a. a- +um oh a-
) tn -n') ' whzne,4/a
syrmol:r) c a'nd gke, *yn a)";c -roo,Lt'jx-.
pnoo,Ei l,-,e,L,A be o
L4en"
A 1;(/t'n')-
LLa, l'qu poR ah- A .
'>ar1Lr
e o, ott") ,. .
SupporA
"
B-- !(,0+n,)
c =+ (A,A,)
"'n-B+c""..@
..,u,,l+ U.Fn,)f
--tr1r'*o';
=iLr'-u't'l
-- | ta'*r+1
-D
t-t t I ',t
Y nw, c
t1)
A)) ,----"---".-"
L!.-+ ,[^ ,, C
-
zkew t;lwt e,tfi 6.
-n')7
(A')']
7Y
- ?-t
L.^
' 1, r'
th.f "/4 Fron e !b
A }* t'l'-e 'tu'
ny'r,1.[t;, m,^tt))a'
,Ur".tuzray+
*.+t I
-,---?---,/'
6 t),*-a)-1"*: /qJ ^"iO,
a)' .$y m),uli c ar,d, -ak<-
xy,"n2t'r) a
,Aew ' 4Y'mm4-Irte .
Srch tJ, g -
i.h!,
"),q_t
p
t
tl orr) 2P - A-f +)
p-+(na*/)
i^;loly , 9. I
(A-A/) "1-t(h
^h'w',
/,J *vre
anly o>,,L,woy o/- </pte4u.t, h A tLe Aurn o,t'
^ynhttte
o'rd -x,(<* +yr^nzJai,. r*trt -
A.^,+ut',n" Pt
^
"Qt i
a.
e+q)' = P't Q'
n)=p- e
M,i)
l
'l
I
2
.L
-t
-1
o
b;"d n-' Lr."tJ
]
.i,,
ti
G;u., T,n
.L
-f
:l
;)
deh(n1= 1
Z
a
tlo
L
'!
a
o
-al + J (a-6) +t (6+1)
.-d"*(A)--
Co-bocLor.ts A,4c
:l
-"'l
* l.'
lr::l
I ;l
*I-l
-ij
""1
'.1
-r a
ll I /
- l, ol " lt,-4
o o (6n ))
6 1a-tI -@+1)'
Q,r)-(o q (a*
] L
'l
.]
7
oo
1.
=l
--LA')'
'li
I
=[;
..na.ta)
Io
-L
-] ]
4dj(4)
J<*Ln)
?,,,"flr )
o
")
'I
b;"t",ln=11 o
Li:
ThJ',
'li i
L1 a
A
G
li:
-li t
izl
qL
20a;-
>oL '
,
jhz
()
o
L
,!(t-o)to@+o'
L
"l?'"t
.L
il
.,laL(n)-
'- W(A)-' *tr :ri
li ol
.' Co-had.oP ae A)
No-,
-:;
oo
dl
+ ao
Itr
"il
"11:/
'l
o
L
at;
;l1
aF
-1
1
o
1
-l
-ttlALj(rt)
-
(0" )'
Now 4.1;(4)
WU)
A-1
lt o ol
l-L r o I
L-L o ll
i,lf t o o I :r f t
l-t t o i / t
l-: o-r I lrLr
rlz o o)
=Zc> z ol
la Q 2l
L-
[r- o ol
lotol
I o o 7)
^- nL^
lL o ol
: I,r t ol
L-r o t)
OZ
o2
o
a
-z
'[i
liL_
9/'
1tn co,!cu,la1=-
Ya-? B' B
G)""n
w(s;, L
.*'I,h
l7l2
,l;l
c)
a
7
2
()
:l -tz:1.1,.
:l -li:l-li:l
l
il -1",:l"li:l
"l?
D
zC>-")
B;B'-
1 o 'to +
':: 3
No-
-, co-,b-o"to, o)-
-1"-
4
r q--a)
'-.1("'o)

'+fo+ 4 J
.l
@-+)
-(o-+)
LO'D)
-+
+
o
-+
+
""J
q.
+
t;
vl=+l
,++
+- o
, . nLj(B)
-
(p';' =
Ngw,
B
-1 ALi ( B)
t
d?J ( 9)
-+ +
+ -+
(a-'rJ
o
o
-J
)/t
J/L
z
. J/L
LL
.t
1/z
.-.8-) B =
I [" "'f
l.l , " " I
] lt z a-)
|"
L +o*u
- f ont* o-
Jo-',*t
L._;-"
-z
l,
or o+L
a+o1D
"t",1
ts9
.E Fi,d t)."e v^luu, 4hd2a- v 7
,L
t
-))
G";
k'
/ *-z -r z),
-n,* e.z./
$;ve thott
l-r-, -"-.)
V-r e+z/
i)
5o,l!',
@
@
q. gd,,@
-7
-z
/r.tdr 40
-7-
-2*
-*
-.57
LT
-7
Hene,wz ye*..,
.1/ -? =
a't}" C X-7)
7-t = Lng
aLt=2
- l 1 ,--
€+? . 7,y
= 3- 1.
/T
.? @f
*" t"j,
y 7
--i
2r-G3)=
i=1 et.@)aan J
3-1
-( )tt
!4
1.
tl
^L
2L+3 =2
.t- L
guJ ry x=-L ar.rd Z -
-3 )n e{
C + (-3) -_-L -y
_=23 =,a_!
eY=-3-1
A-n,,',z -,_ L, y= ,4- ,Z z 4 & *=
@Jb o.[". ,] o,d_s fo
LJ 1] L'
Aho,.t )',"+ /n, o,t,, , 4) (p B) _J
",
-,t,
' -f
-'>r' / t,nLv?tr .f4":rt -/_
o l: ,l B l" 1l
Lr 1l
lt .l
Now,r' 8-1" tl-lo sr
t t't -l
L' rl l'ol-J
- ta I l
I -l
L2 )l
:l :l
,, (a+B) (A B)
L:A-e. f o
Ll
'LZ
,',@-te)(n ",1
1
",1
.',-[Z:]L:
- fo* o o+
L.-, o+
-Lz
=Lt
ta 1l
la ol
f^.-
- lY 't'
LJO]
-
| o +1- |
^.
-lo.)l
I a 1l
Io l lla
l1 )ll1
Now,
^L
h =A A =
:l
::;l
:l
ond_,
B-=.B,B
o* o )
, * oJ
o--t-' l:L- :l'J-f.2 I lo
"l
=
f:
''(A-B) [A-B)1P'B'/)
"L
l:
t:
I " zet-11.9
Z
L
J
o")
. Srnvulot olt I
I
L
=1(t-*)l
+
z
-+
3-
-C,,I'i
2
+-/
-+
3-t z
2 +n
) l-9 +a-
LPtt"'et
'o-lnz
"5 I , lt-
-J-:
o
-ta*L/
ap /
2
L
=o
-
G-t) Ltr-3,()++t
2 3tt- 9*-zi-t3zL=
=)-ti + Lz.a - g tt --o
.=>
-/L L/,--6t+1)--d
7Q-,t) l-* +x -+r' * tLr+4) - 2
a )L ('xz 2 t 3+jL). o
( t-s)---o
)L= O Af
(: zt)+7G
o
(-Y ="
+ )L-3=o
[=un
A^
/Sa
yaXtire:). v o-[tu, oh- tuAr3*no*.;L
inylar'
i.,r-zcir- equ oj;on
,A-A^^ :
S,l'ove *l'?, ka"Llowiny zy+Lem ob hr,eqv
ecyro.liair,rb .",,'L L^< Mp o)- .^oLr;x:
zx - 3y -r'9-z-L
?x t+Y -tz --to
r .17.2?.J
lZoogl
t* Gi,en hh"J.,
21 3y ++z --L
3/ ++y -52
-Lo
tf - VY -rLz -- 3
e.tnoJjonf ,n;tv'z-u'-nJ x J'a?r a'Pe
6eLow ',
'Te given
"/rrtte)1 04
Con4iden
to,l
Ax--$
.',X *A LB
-3 +11, 1 frl
: :llll l':l
"*
ft
l-
l1
+.L
-12 -3 +l
-
| z + -t I
l' I
l9 -7 zl
= 2 l8 -3t) + 3 (6'+ 25) + + (-a-zb)
- ZCLT) rQ { 3t) + +(-n)
-- -5* +9j -16q = -LLt
tA)
/ W (A)---tzs
Co -b+1'to'n 6P
And,
A Ac=
|i -5 |" lv
-l
"'!'l
2
t
nl+ -5 |
1.7 LI
- I-3+l
l-7 zl
- L-l e+r
" (e+-?r)
L+- zo2
- (-ro-u-)
,;]
-lz
f
f ? ?q )
/1r ./
-L7 -3I
^- -t "t,
(e+e)
,"At4G)--@)'-- -"1
:+l
,11-),4.
|
-,,
-n-
L
r+1
J
,1/
l,t
_11
-]
22
r']
4A (4)nL -
A.'B
det t rl;
illi,
i)
;l
'^..
l".ltv I
LzJ
I r I - [ z't
[] I Ljl
Nou,r,
'l ['l
,"llvl
1?) L3)
?,1.L ,.1
, f -rz -22
=.,,t1- J, tL
-'-l
I _4r -1
L'
t i-tz
* zzo-
-;-*-3r-LL6+
'"' l-+t rc+s
r f ,sr,1
- Tztl-ttr 1
lo J
*.L;
An)
J. Lt7 o
I lr+z)
I t^ .., Ueo,o
ff4SLore Lhe l>r-urcwtn&
'J,* *ya d? ")'
lJrir
"/-+Y+2 =4
a y+z--z
b{+y_Z =L
5oI"i Gi,en thol ,A:e
X+y tZ --G
l-V *? _
-
2t'+t-t-^
-Tfr4
$ven e{ )n *nz mntr)x
-rjlterl
69 5-taw I
l" t tf rt r r,-t
l,-,,ll!l=l;l
lz t 'tl LzL y4
C"rrulq' hh"L,
Ax: p
.',x= A'B
Now,
s4rraL l', :'1l
t"l
lL 1-rl
'-l(r-r)-t(t--'r'
-- a+3+3 --I
-'.ld(n) = 6
/
-7
1
l
l
-/1:1
i
+11
IL-LI I z
+lx rl
-ll
l'-rl It
, Yo;Loe o/. t., nc- ::l
iilf -liil ii/'f
t:
o
Z
L
33
3l
l
'.t
j3
-1 a
a'L
=17. nq(n)1)'
Ae.j( A)
-a z L I-t
- - |
l,
r., o I
ll
l3 J -Ll
d"t ( A)
7L
-3 a
t -L
=iL:
N,
X
a1
v)
f *1
lv l-la I
L')
til
,,1
l
2
z
o
Z
.Z
2
3
1
6
.L
l
B
lo
16
6
tz
tt
-
1
o
J',
.L1
T
I
L'1-
7
3
a
e
T
r_[
cl
L
ff
7
L3
v'-2 4z--3.^
,p-
/,.ib^ +l-e ]t1rcf)e
,4y ''
I2- ho-Mb;u'). e trLo'ub
Jl+ eY -r t =
2,t-3Y + Z =
-7 ++Y+eZ --
GL'ten hh*t'
3t+5>-+z-- 6
2{_3y+Z=t
-L ++2 +ez -'L3
'tl"z
$veu ey*l;au )v tw 'mJit' Ffo'n ate
,s.p'alten 6;,' Le)aw I
t
L3
*hz, eo et*ic''"xI
El sXove
pJrir
9o,1"",
-+

e
],ilItr|=L'l
5
-)
llL-'
.- Y A'Q
t
3
+
Coilza Lhol' At-B
'[eLLn) '
l1L-' !l-, 3(-tz - +) - 5 (12* r) - +G'3)
<t-24 ) -tt-.. 1'2_
- --/ < "j
-66 - 6t,za
*l:
P,
2l
':l
:l3
L
:,'a
- (:rl,i i)
ue-+)
-l:,
-.L
trs)
.l"
, ,tr,t (4) --
A"-l+
Ag*",
Co-bocla, ob -j
5
1
-;l
:l1:
/-re-+)
-ho +je)
(9 - lL) - Lj+t)
"
. /
.',frELA)4!').
kl
I
,il=l+
il
L7
:13
5t
t.l-tL)
-43
au
- 11
_ L'L
-7
-13
3+
-11
- +L
'5
-J1
"19
t
,- p-t -
444( a)
a+
-1L
Now
x- ['B
dekLn)
L'L
-qLr
dL
-1
_+L
at
-z-lfe'
" llr J-LeI L13)
t=3 : ! = l 4ru
u4*, o,p- <E4dJttth4 o)1
1 l-i"32-z3D-e1,1- 6tl-+s++o-t+3
l
I to-zs-z+z 1
t-
t l- +szl
tuI-ta l
L-3aLJ
f.l f z1
'1rl-l'/
L*J LZ)
lhc.k,
Jr<+!y-/7 -,13
+x +y ,122 -- 6
2/ +9y 3Z = zo
eqqoho,, )n k ,a oI ',L ,t"r,n
-^lr t 11.t1 fr1 )
l+, -'"ll/l=)"1
L, e -]lLzl L*J
E 9,tru" tz b oilo-;"y
rnuti t mt*hod i
3 /-.+t/
+x-+y
L'( +9y
-7L
-32
>r,^ r n.verl
1e,
?jtven
a oe ow
ean be g1"q,
I Cor,,jJtr/:'4 |X--A
-''X =A'B
(n)=
*)
d2.,
lVa
l3 5 -11
I
+ L -11
|
Lz e -31
+
-f,i
+
L
3
2:
', jt'l il
tt'l
--3 - t L- r" rZ+)-7 lrL -LJ
-- Qttoe)-Qatt) -@xz+')
- (o - 23t
- 1e3
(-s* tos)
*lItI
-7
-ltL
-3
-7
-3
^O-
,-'Co-foJot 'k lL
3t-l? -7 | +
li .4-7
-JL
-4
t)
5
3
2+
I toa
=l-*s
luu
i,l'[';:
-+3
t
Nl. _,
X
709
_ J't-
7+
= 5J
3- 17 | --. I ; | - l1
tr I
Lzl
It
.-,Ati@=@r'-
-r AU(E
t& G)
1f Lot
' ,:.- | - a-
I z+L
-_n"B
t f t-ttv:z.38-ra 6
)7
l-
IeL +30+ !6u
I .!+2,-roL - 3c-d
L
rltrl
-"Lo )
f 1 I-,_tr1?_l
LAJ
-+,
t
-,1?
- 13
3
-J]
aj
(
LO
..'.r--Irt=z 4V.u^
z2
o- )y1irfl4/+n(
v,) h4.e ' A -
9,f : Giu""
vie
@ fuPretztJ'e'v"J:t)x 4 "a l)'a
2il
c',rd a
l:2):q"*t
^'Lt,
ii2'.1"[i: :]
t'
ts c -3.1
I r L -6 i
L,-, -*J
=V2-':]V,i,;]
-L?T 3Jl"l
cz L .o)
zke
1l
f + L -Y I--1a i. o I
l:3 -L '7 |
-)
,',A,
LLeh)
A+A,.
d{.,
A-A,
/
4 4')
*[i
;,1
,'il,
Llt'
!, ( t+e') -t f't
tls z -s1o
Tlz t -e l
-, -b
L
l+ 31t -+1
lz/z t -1
|
l*+ -3 -]l
a) Ah-A
Ayhrwt' e
4 q o.b-
tnutrr>t.
f + 2 -3.f
l:L l -"1
L-t o -*J
,1 -a4 el f e@l
qn l" hkewytnw/ ftc
_
I tgehva^u44 I E;aan
",o"7o_,-.--.,-_'.._,,
--r-.,:__^;zFll- n ,,,u UeD-Lnz <
ch q*otler;4Jic+
Cho:,acIe,
^,yL
r+ polynom)J oL t -4qt<qtq
t"*'' : 7*.G-E""t^""t l4
wi4 $:ve o polyno^ioJ", *ru"n
)Il ," hnn
".p",an
c^qYqaLeqj*iu polv>on;^J oa o-
For ettmplz: lc_.
It'-/ ' Ilr 3-^l
_ Cz_DG_z)_ z
--
e -27- 37 -1,>"-2
-- *-ev- +
ch q'paatefi^liu elua*)ot lr cL -.L?Qqle bq*tt :
w e cal-?, w
8LQqre ha.LP;t A.
'fl,e. eauahon I A- )Il =o ,i), cuLI-zd,
l12 cha:r,oaLe*h4 eLuo*;on o/, tha mfrix p .
As,, ;i- 52-+=o
e,yen v a.Luz-.gr"o,blzm'
A be a -gcLtrar
e .r.aoirirc '
"i,/-h
etz*,en!* ato'Tt''*'* )L
,. ntolrt a YrLtmb€)"7 o'vrL
t) o, ' tt-"
^w
h )-hJ.
At - VLL . @
W D"Y;,^z'
gJus", r
6r[er' " nu
a-V;t7
9.b thlx
zaxo vaa
f trzh;
V- E
49'r, vauz a-r' ]6Jer* rool' on cbdqaj'r
'z)'
u' v
"lY<
'
u -: Eigzn vedfu>'o ot' chaYqakv'J|. v<c*on o'E
tv,zn r'."4'
I ror^ eqh g., "u e gd.'
[q,r , o,, %,) u - o
t-1
l l',, %z-.7 a-2"
q,, l
L- , "",
t
o,' o
".,,-,/
9t r< pre,rarita 4z* ob hamo1zt'eou-t"4"*;;'|".
lA-
zI) -- O A a' po,(yrv,ar"iodQaLlo}ja." ob- dgt'< ' n''
)LTf", Z:
t a-afit
Now, chqt'q6fs45/.;6a, p oXyr'avno
n--lzz ,
li::l
L lr- A)+a'- 1).a
f L4
-) - ^^,'-z_rL4
2
z
u. 1
/-tn ,
A'^a= l7
ll
l"
=l'ilt
)t ch.'rq oter
z i] -)[e ool
^ . I l^
^
I
r 't t" - - l
q zl Loaal
:.1
l=o
l
l
I
I
2-2

L
2
3-)
2
> (2-v)IO-v)(2->)-2t - 2L2-2- )
-+1(z_3+z):o
) (z >) (e-=t - zv+2.-t_, 
-/ r
-- b /t - .t'h
+ ZZ- - e Z-+ j*
- ++L2+7-7-,a
-.'-.i'
1!i'' -tt-'t +t-+ 9
-
h'' 4 - t)'t tti-e.o pt t> tor,Jtprt&c -t"-
E r=j*4
" ,J
"- f chqo cfzr'aLa ^roo* !
We l(vraw IA-7Tl= o
4*-72- rttt'-Y = o
=>
^"
.'>"- 6'),.+t) + g2 . o
=>z'0-a),n [], ))+ e(x_))
)4 ,) L2. L>,r)r o
) O-1) Iztz-s)-t (z-s)l -,o
.. (z j)q2.11(2_9)_
a
,'V-- .t t_,, ,2
.'. Ch a'raa*erLhi.. ..ao* ar E;gzn y6Lu-ez
oY 4,1,5 ,
I
ts
s.{: th"+.,
,=F
/,h-< elsznvaXua
*zhvec+,'rJt o,,
tl
l
o
IA-
t.+
?1
qnl, *h<
*h-z '".If
x
:l
ch ar acte,v,i-iu e g)-t^l:,ian ol-
vTl-a
-2
rl
)
'ro : ,,1
@ 4.@'
*elt'
U.* , 1", /'z' be kL-e eotl P6nar'l 7'E
e'r'yznuer*ot, .lqJt , 3=[+
ca-ne^pot'U4y La l-a etX<nuJa
t^
L/-t-)rl-_a
=>lr-^ n ll/,j,=o
| 9 t->l!,,, 1
L
) L- -)
rot, A-_ - b,
f t,- f--E) 4 )r .'-
l- .
"
.ll '" 1'=L t L-cr)JL,,J
*- [a +lfz-t
1'l9 .ll , l-_o
I l xz I
,fl"r.e-/r1=1"-l''
L9rt.6,rrJ L"J
.- 6aL+Hv-"-o "',.@,'
2lr 4b(L=o - , ).(D
-IILT e A yr6 .A olu*jo r. o /- e. g
9otf-or 7r=o ), ey
@ , ft
^- : o
'
.--- I
e1"Aq@
dW.j 15on
)
=)
fle"ez, e)yen
F, r 'A
-
])
"/, ) t^4
-.-@ ,ll t.
q.l/.,. a
(/2, E>-9
'/3
2
v<cJ"t. .'>, /
^ u)
, L
>"Jat"" oJ-
@ *;,1! be'
,)
?).
)., IW ch a-aatt<,rL';l1I
-1,'
Lr--z) + I f- -t
t",-tl
F-
l-: * | l,' ) -
o
L7
.O]
L'J
F
l-LtL ++r= I
-
t:,
L 9rt- e
". l
'x.-9-(
-o , (?)
tL -6/t 'o " '@
-)
-)
,., 6
9
llzr a *t
'9
o,a1"
-( n,
-2
@ 6L1't te<
tr:J
tt)
YyAI L
I
(t- >)|cv"a;O )) - J1- tgt,z _s)+s(L-1,+3s)
=) t t-t)(9 -,)- 7, ), r) r 7/1, -
' t t) )1l+ L),') /..),2-,)^)-;:=:'J1
t b
) ?- { ) +)'- +2 -rt).- vi +j6) - Tb = o
:, - )7 -t V)-- 3d --a
-
)t, l. -+?- - o
rthd
v e.cLctY
^
So/"I Le) ,
A= l;
lz
Now, c hqaaCle
.Lh-Z L.tzn
oA th4
v ol uz4
l"L-
qnd
1
5
l_
rJ t4
11
'l
I)
3
l-
IJ -))
L
irl
plunan:-L
(x-))
1
3
Cn{'r ddtey;riti L c-:q ), 11-zt) =o
-/ Q--?) 3-
x E-z)
JJ
A"V
I
t- r)
),
/
72zt, 2 z' -92' - ) 8', tgt, 3.
)f 1V,t,-9Ztt- ,iB(t- zt. o
t Q*z) (h''.t7+ ts) = a
(h'- 6) -3)rn)_ o
lh0 q-3o-(,)l=a-
(^+z)
t[? L)I
Copre1p
i1 -
to
)al ",Llu< )
o&u
ox
'lQ-z) (h-2 ,o-rr- o
' Lr 5<
,) = -
v6lu4
IeL.<,t" t,y t tLt
'
ahP"r"zt o,h- q'4
t--^ytlr t<( Lo, I xh-r I
1
(t v)
1
3
3.
11-))
ll,)
llY l=o
llz I
:l
rh4
cnkny
ln-L
,t-z)
?
-l'i ':
.'"2? | lot tt1--'Lt >)v*z I lal
L'l +r+ttvl
7l L"l
2-'2reg' @
-^1'l
f u-+y,y37l=['o1
1,*z"rzI l?I
Lt,L+y+tzl l,:J
'' 3t+Yt3Z - o
L r ?.y*z = o
3t+y+32 ja
I
g, *)1 b<,
+321=la1
+z I lalI t-l
-zzI L'J
t-I
lz
klvr,
9;""2
, b;r# ond .tlrind egh
wz ca, ehoatz hr"'k and,
qre zamz 2 !h-erubo'r",
.S<conI
-
ntt
Henaz
'v"Jhb.
-:,
.
- --:- -
1L+v
-22 -^
- r>+t =6
: --, :-
,- J L1,1
- o - -Vi
e)Wn .,re.ioy "r (_1, o, Z)
2/+ y
)L+y
j:herc*otz,
hca r ,bir^tr
.t<
"t
zzjtj 3z
1- LJ
..'r+/ + J L
' t '+Z2+t
3t +y -ZV
Lh-LrQ e.y' at"e
sl16ay,< )rirat
)qJ1IZ
ohl ae.dhleA
.O
z
:a
Sint(," Lt*
/l'tr dnr e ,
on{ 3tl c-ah
w€ c ayt ChaaM
, t){ =A
-x+zy+z _a
't
.l
-- 'l
e1y n
c''fe ,r,,i.lo.Y ,
tet ad zn) ,-9".
L
-t
z
:1.
,v.T
" c:Ju, .-'.1<nr<
'.1 7
_2,, _1_
te7
l;!,
6r
=f: l
LoJ
;u
,lz3,
7
-+2
t -5
w hz'1  _(
,t+ y-r3z --o
L-Ylt=O
) t + Z- rX = a
9)uc{
, Lz.* ayll 3n) e{ ore -ai)e;,iqy,
hr',erel'oy e, ,re c.1,>) cotual,pt, Jz* Q ZrJ e r>
' '-e/. t'Y +32
-/
-
l
o
', I
Hena-e e-4kn vecf,o" -i. (1,1
Hen tZ
, /hree- e.+52" Ve<*oy4
Lr,- L) L) dnd-(.1,,z,J )
Jtu.-
rr3 2*- ' -=---
,'J
9?
th-e e'+'.en
notlt>t , 4
1)
aYe (- Lro, 1)
v)< rt Vecror^ft F;nd
Dk *hz
VaJl)Le^ ct, d
= lE o 1l
lo
-L o l
L1 A
'J
-1, o a l
-t-J
lo -, ol
l1 a tl
$ G;,enthd,4
I
c t)ot'aOf . r^;L U c,1u o_lr'a1
>L5-v) (-to -t-Zz-t) +2].)+ 2+ ) = a
a L5-)) (z'-sz-zo) + 21v= o
> 5)" - 1t, - 50 -x3 +3v. + ta)+z+r=b
) -)3+97'- +) - E3 = o
)
-r3 -gi} +,1) + 4t = a
t 2aj Zh" -1bh'- 762 12+a +
-; *(z*z)- toz (z+z) t2+0
-SQvz)Lt- - 1oV+z+) --o
f>+z) ()'- 6)-+, +2+) = o
. ,)
(
"'z)
1ltt )- 6/ .+ /1-b) -D
L +z) L-+).L^-t)-o
2---2,+,6.
t lntrL=;
t') a
o - 2-2
10
a
a
5-)
)(.))t( 2"-1/(eo)1-o Lt -."./.a
, . E,yn" volu<
/../-
't e1*o y4
t, be
*c "j
i!
Lr e)- .Lhz , oa pornnt
ti:l
&Jz.
aL dh
I
I
s 1l =,V xt
@ be tuhe^
2.21= o
Xz = o
r:.1'L^'l
e44'
c)
1l
:l(et) I
.El
v
^,Iu-!
ndiay f,o fr,h<,
fn-ar12 =
Itv-z> o
I" cz-^)
I
l,t o
LE'))/, rt3
1
LL-7)/. I-1
tt r(v,z) t, I
,J
-6rte.4po
w h_!h
tv-
2 eL"@
f7+L, a
L xt*/r,
I-J
Trrrxr=a,
.') + l(?=a
tar ravo €qb /)
,ri-!44 a a].
7
flenee., eorrlpond"vy et52n v<ciot -a
-/ -l O I
/,) -l  |L",J
 il ll l-
Anao V-*,er/'@ ^.t tt('
frrr,"I =f
" t
I ^1,, I l" IL /7-t/3
I La-
.,)tL+73 = o
,Llt _, o
V t +tr, - z
5,n(2, Ll.,t + 3.pL et-
l^JU Cqb eorv,.tJet la* 4
/Lia|. a
-61, =o
7L
--o
T^1", y 1.,. h ):1.<n /, _
so, teaar2s
v ec-ton b, ,
W lre,
, eqh
t- |
4anz,Ihrzre&oy"
€ ,Lb,
'k
f.=
Ltl
@ wia b<
-1"1
L'lr:"1
hn , u,t
taLil,tt,
lne-u^
! "t
o"l, =
.1_ 23.
J 3r)
--n
)4 +,2-"s
P1 - ^3
_b/t
nz
-o
a
o
))
et"
-1.fin
y 7, -, k ,
5o tl'p, 1'aqQref,
)"
tb )1-)
ve (taq .?
/La , 42 =141
?ov
ft'L
-non-*Lze I
'v4.*a'' x
eitL,
-l'l
rz)
-=. J
v
"
Jon,
.t)" r-Llz) n orm*I)>e) a>
a i /:t/ barmdt '
tt, 7r" -+ *') + t,
fu" )=-2. '"')<'
4t, =
g.ot ,:Lgan t<J"-naave-
LEl
"ndP'r^ol;zee
o'+ A a
v
"
rtor,
OL'. )
)
ta kaY
/
Fay, are. g-ot e)gzn t eJo, ,)-u
x''1
hoeryq!;r-4 ery<nvel",Lc4,) con-etpen&nL
foJ o" l-"1
11,I l-) |
la I lo l
we,h
.L:J
)ot 6on , "-rLud ,.Ju.,
kt+ Dt
L
I
(.-t;)'= Z
)
,k
kt=z
.l
,'z
d v<cJur,
eig<u v<c/o,
co-r,rezpandiny -not1act!i2s
K + o-+ L-t,)-=1
) zka:1
) t<',, r
'L

""^r1-
.crr apooh4y n qrmali z4d-
I :? I or t- L l
| "_ I )t "r, I
lel ) p I
L ,L
I t n, t
Hen.<,
Her,c,e,,
etSun.-L
ho,ve lDt
=r:1Lxl
For, V= 6, v.'e
8,
ve/-^ut' ''r <
So, bor not"mJ;2aS vec,to'r,
R'no-+k'=1
-t k. = ]t,
Henez. conr'.t,p:r:"y
_r,oo
r.altz-zd
lj" I ^' I il
lo I lol
L-il L+J
fier,tz-, *tz * r''na eitzn /e(tar
(o"t,o1 or (o.-)''/ '
(f o,
(-;,'-i),(I o, il
.i
(- i' "", l, /"
:2-
o't>
or<
l
d2 /
D -/)
-hqunt ( ,^ .f rt-
/'^ .tl tl
',v9
-ay na mLtIoh laot" rn i Evet y
( o Jt , 3LtL,>^r<4 .4
"n..^,r-
< h ar al<t;aliq
e{ [a,zt 1 o
Uh Vefl-b f <ay,!e.y Hq-;JJ"n *hzorcm l-o'r
t'tz v.,J,)n ,
A =|
t +1 ontr /)v L ).14)nve,,e. nho.
lz 3l
etlfe
^
A5-+4n-763+11k'-A, joT A d
l),
lr ^taY ? a)ynoni J )n D .
SoL"I G;,r.n kh,*,
f 1
't=lL
+l
lz 3l
Wc k na-,
^l ,
cnaPottrzrutkc4 €g" oL ^6-I.,t p
^,
I A' zl l =o
" lt a + t
I t--o
lt 3-) I
l- t
> (1-v)(s >)-3 = o
) 3-V-:t+h1- B-- o
.,a--+7-r=1t
*7 -T=6
Aho^,, l(r])-o
be,l(4)=nz-+n-
aA -
CcLn
,-,+(v)--
,4e ho'tz'
c.; t(r])
Naw,
n'
L,H,5,
I
[,t + ] ] + l:nn -)1 3l lz z l
L"-r,-l
-r*: ++)11
'l''t s"'I
t,-
=le '11
L8 lvl
,_A', +n-5r
-lt xLl- +l' "l -tl'o
ls tt1 ),2 t) v
Fq
'-l
@q
"l-f'l" iil-'ls ),1 rn
9-+-t
16-''6'"1
lr-,-o
tt 41 t)
L
lo "1
LO "J
a,H5'
o
o
-J
) vn-
l. . r.
, wv. dJh
h (2, _
(z--+t-v2
yt-+ze-vyin
'lt-+tu- 5vz-
.L:
+l
-r I
- n,rL
f)' - 7 2t -t Lt'- 2-taI)
tJ2",2-JoL
zvj -r 8)"+ ) o)+721-J 2) -) t z
+(n+tr)
::l
':l1
3
,t
2
t
I
1
5
il1
low
L _--
9)yez,6n2 zoJrtrtq ))' t b c-,"a,t<-74k4 qxn
I u.,it-,. q
AL
>A
4-A
4
+I 5n "-
- A- +T
L / a_+f )
'
'' L^,rpo, go,lyno"-*,| 0.)r
LIfta- a +wL) )n r) n
e A1 ;L hall
(n9- +n+-7ne+
( ++tr)^
g-
Gh,
'L "t
,+ub-mJix- oA-
?4to"
fh4 1.ta*Ltn qra
.fto have Yqnk
'in )nua'"
v7(v',n- 5)
'J(n'-
-L1, (v'-
+1 r)+
+n-9)
lx-(d r.)
-f
L.fl Kqrl A nan. 2216 7nJ' x
6rl4t
an?
; W.F<ten* ,b-tom
NQ
9F A U. ar' qr"bi&a',"y mxh molt')x 6veY
o. k'd L F '
"fhz- ^r'qnk o/' *hz- "'t
"t)
t 4
p ,/+.t /"*y* v
"'luz o.f r -bo1 w Dev, tun,"
entl t n,n 'Uj.b'mat' * ob- fl *)tt" non-
yonia}","rX.fu*evnun">* "
.l
ILu"t o r'2' oJ'T
O8
In2 ^fa,nK
',tL'r'tbet o f
(o/ uY'l M t Y)
ok*vJri-Ah
h",er), in f,<,pen{u'I
ftu'e-"nJr; t
y, o)r .modt)t ,
o.ndA*@
j"'e,Le^lz ,Lnz , ou-z ua )
/90 1:ha-t th,z efln, 2* +3y +Sz = 2
V,, t3t.2t -B
t* u6to-7=-o
hova,t) Np so)ul;o, i ) a una"z -+o,lul-ion
6t) frn i #;h;Jz rl kn be). 0,6 z"/ul; ., ,
So,la.' We hoveA7a-r+
lz = b l f 'l
=f ?-l
lt '''llY I l')
lz 3 )lLZ) L')L'"
rnz *y;,tzq ho5 a-rya zo)uJ.'on
j'b
,an
d a 'v
i,b. kL cct- e|b) ''te'rt '"oh)t
jt oy l qnk e I'
NlJ> veqrile4 Lhc*'
? ? 5-) = Lt(5,v)+oit 3 'zl
,L 3 ) l
tt"t kn LLiqa s.],,kon ) {! ot:d- A h"v.
Yave qny
",iue.
Jb A t ll'z z y;y'e'm'tu
hoverr o s.ftli" ko, /v. o'r<'vott'z't o/' U 'L"
r
w l."eI t!.2 t |'tv(4. 2
.r''.':'-.

*
""t=
*L ,l oo'nz- Y* Y. Bq.t A ;
"'u
L Ant B, p nat' a/s tank 2, w),.7t"a
'Thut,iE A=5 anL )t -tI , frLe z>,/'^
ov< yro 1.,o)r.L;ot
^"
L ,* A=5 crnl
ko ,:rtn-
-/U
houn a', )vb)n;]-c
o), t"Jq,lr'ow.
ft=lI
L
qe 1o
-f orI
LL-,7.
*;Ll h
Ut?,
I Ltmxr
Boulr
L IYEqI(
ll M0
^,
n 
{l}qe}Kq-
v rd fl q4l oahra'/
I
q
A fl v^RErr+l^.-- Qra+nix()
1n^f{'^^+J *"+t"A^-
|
La.{'ce€
--n<n'{.
S
of n-lr.i
"s
csE- 2l r
ri a3 12-.
RI K
-n*".V*
l
4,".)i,4<it.
J.
,1 ppcl r^r"ki 19 I + ?nii- {rrr a[6(1 '
{.
E'
Exa'^e
Eohd" [Aa,.r
- - - 4d
ooh,r, 'o-' Ta+nix-g I ?r 4fl.4- oat"'nr {lrr.(1
tio,? '6 I l' l
l:"1I E) I
S+*Fe
-^^+",i1
-'t'f
""^+t;n-
ct gooq *!"-i.:f,
<rao4 r,:L<n t!.<
"*
t"lfl'
F'-.e,?| I ' ?l':,,;JllJil;"K'^
I 1 e
-'I
lto
2 2)axz
'r Dr"go,o 1a'+;
:liopo"-,!. a<<1 e-%r'r'n{
u5]-,?..nO lLt'- o '
:-l,,'
o I,J
am"(a
v
r'lc
lo
4 s""J"n
"o1r.,6
g }l^go"-
1rd.({
:
)
,
o
e
a'
I
,tl (u^il r"vftriv.)
ele'--d -qo1c Q
| + o 01
tl
la i. al
l6 o 1l
,=
l,:'
+'
oa'.:,g*e an"i.ft;^
"1
t ='T
f-j z -zil
u=f:'_i,:l
'e
fr<h " 0
0
6Je".+i3 : )iagcn*t <11<3-
9
vr 1tF-
I
t
Et-^ 3
J
-
:t tr
3
t -2J
A- ft.o.m?.s4
9' NulI halfti)L t
Jo, S$h"Y€+nic )"!r$n
A*a",,t
-.;-: i.".T,r
it;
-1
b-
9
-3
1
Syrlo'€tKie ?r!r+n)
^T
( a e ':l
A=l'::, ;lI
e 3l lo 9-t
, -Lt -_t-9
u + j--tl
. ol la-r{ I.,. I l- I
Jl' SKccJ
r
-l: Herr'i lid' *'Jn
^ '"
1r1 r'^<.ltit{'
irede -6|(r
3C,T4 21 -tele
4(or '
?r?r_ btr(6
1to c-'rPlet ca'.-
'.,q-(.ji- ,.+nr'' c$
ler rl1r-ir' SK
(r 'dni u< +@'b|a'- a<('"r
- A t-4{ 3{4Td
sgo 2rl-elrrie
r^'S(i^ ?<fT
tg.A*
*.*niN
r-:
o -i -<.q| '
.l
. 0 "1 I
.1
?r ' aJ
oflt(oal€- of("r utKdl$-
k-r <kcci ttrrlrrlnu''
1 il,J r )
r' -il
t; ]l
 x. *l'A
L-'! tl'
nv,.'r{io Fhi
Ia= |
L
r! -(6 Ca/hde(
bf q5{r{ aT
e

o
'A
h,
't
i
I
.-l*i'
I
s
1
l
<.(r
13'
1
l
- ^J-
ba.tnlK-; <Ll
'qG#
Ar'
A=B
r. c. 1
t I 
t" I
Bt
,-.,i-
* :Co.Ir* ?F
,.-'1 , . "
-- , h/).npi.Y I
3 -- -
- {'l r
1l
'ai-eara,f1
tdr-rix ?
fr*- ti
l,- o
r -{
Ar|
L^
.J"(t *a{'
1-atnl KB r
.'o. ERIOd]q
a-
*=
3
-C ritnt
eedaAie.
r4, NJa{{v.+ 1'l 5-lc
I
F,{cl*S
t:?,3 -
i
A2
^=
[]
A3 L:z
I
D
,
)
{
{
I
(
i
1
?
-L
A--e.A
o3- a'' e
$|"r-pol"d "-ls,i,t',
8 K= t,:, 'l ' "
<-a a1
l..t
n: l-r -:l
L
Fy= 1 ,il^.(< ,l is '?""[e
i"'a+i!'rv-
Ao--A R
T s a-
')'
|J r^"'{nit(
-rL"
tr. e i&r',tok-t
'Y--{11a.'
-0
r+<,,s,}qrry..d,.iy.:
]i.nlrff itJi'
$Jrle7
w anr
' ' !.<ln''y. qm'
s 1=o
s1
9
l0_
t,
Non-si.6rrr!*n
r:, Co-5^ul"n n *ni"-:
5{"*[,
w=
le* t
(3-jqei€ n
tI r."lrnrv-
F'@' !
r"+flir1 G{ AekQ'',4q qq
qe(6 ^d-sitde.f r'c'1[l^
Qn;a I -1'.r
:?,{{- , a. .{t
<<fr;,
ff] *o
. e al
1 2 ol
, a',2 o'3]
., !
-,ilo.aq "*1.
I
I
-"'.t
^J,2-
a"lj
'^xn ..
,;af an =An. -7 co
t1 'a1'r = Atz
I ^'rt^
/i'
l"'
$,.cfinAb'
T
I
'z ai
CoiJE('b(
tr
- i""F".!"t-l
a
I
)
t
l
J
L''
J
i
2 --J)1 =-,
-t{ -r-f r ,q::-")_'-l
^ -l- 2--"
t --/
, - l-r)"n,'3 = 3
o, eJej'€'^t
*.ni* u! c"-J'.cJ'rc |
L
e* heioK 4 a.
"o.lrLl*t
A
t. *&-j"i* i^"*ni"- t
nAt.in r",.{nirl'
'd
f
t-
1=l
L
-e1
'l
t-"'_
Srr
lll?-
a:
aJ n= 63j
.atnix-
'f
rnJ
4'
lr ,
$-r$i"r.s<
$^',er.sd
r".nir- 9
"-.r"t
at
g}1(r4)
= B+0
-1 l I
6<-a6 IL6iue.'il^t
D= $
o.eE- 2b
ai < t-olr,,],q-
trJ.'i'(,
o
3
2=='
c|e+€fLT^l
rj
-l
6fr{l
L';-d "-
rii rc;r !. *Le
3
.r - E{a-rr))-1,rYe-(-'J)-*3(r.' 61'rl-|../-/ ,/ ,-/
2l:e+]l+34
2
.1
3
1 o
:t 3l
l, :,J.,.3 r /
. 1a-'J
t+rlt -rt
Arr:i-9 13z I
:-(&3>-r)
"
2+rl2 3l
n:LL-1
') 13 , I
,, = 1-2 =5
F-:{-9 /. _,
- -l-'- r9=
a{i: -(.r.r
l*.{..it- .sf,
^lrale C0 _-i.^A_l{I
+
it lo ,:rI
A$:t) lr . /
= [o+r't
?+l[- e I
*1':{-D i3 '. /
= _(-:i3lr
3+t._l] l
h,tV L_,1rl
+
Arr=tl),.
:+
F.33=(-D
o
llAlnlv,{
^L
8-fE(](? =''-J' 'L qJ
tzlT h
;jFE
1.3.j .
el
?d I . -
,1
r -*lf
"-I -rLl | ) l=
, -'=lIa]
u
-5
",9
--l/
,rl
1l
lY.R ae- dJ oSlp).J
lA
-",.,1'i
"J
I
3
l{
Giu.n-tt.e =ry$g-
3K t 5$ - +, --i3
1xt9-rr'2 = 6
? %-- 3Z = '<o
lr^. t or'.rx- {.*. "+
*te Qi'cn q1'*t-:
n
a
:) AX-- R
6
I
-1
L-e-{,4= - ti
F",o.," 6
-l
.=?q,+x
:) TK
)'x'=
l+..'*r.
3
7
I -'
1r^q
""{"..{1
o} +
4tr -- 3 f io& -- lo
42l = -Ll5 +e)=-*
&31 = - 60++= 53
'I
t-
L
z)-
(
J
- -'@"
D -IAI
- 3i --5 +16|r/ -
, +rt--(a.+t).4'-1'1=,A',2'3 7'
'.:
39
_tT
-tf
-
)
)
I
rne na3lr] a!(6)=
- lr
5
*
-1*
-7
- la,
31
1f
l
-*lfol
"/i,/-") Lr"J
ilo,l
L
'lit
f
;
-TI.e trrvot+e al C = I ',u
/
-
''
L'T
fi<dnO X-A lp
lrE
7+
31
.o
.ej C€) I
1tsr1
-t7
T
]-1 ?=o
:!- 2Jq
Gi*t
.A"t-q+*
/ U,r- h,bL
R-P"
ol
^l"/
,
+
()
a
o
o
O
T
-x^€, Cr.,-"tro. $t-" o4
-
*'*..i s
,t- - f z q -!1'r
l+r,l =l c ;loL-t l*l
It
5 -1 | D
i,
o 314 r
L. ,1 I L 0
'o-;l
",,)
*
[".
R{
LI
t r" -1c {--[{ ;
f:
L*
-1
5
) n'" g a'Bn
*"1.
J, e,,xt=u .
t"/ ^1x'- 9r'
t-
F2A{-- & K1'
O LO
-L8
a
o A -1
o 1 <t1
I
13ol
I
r u '_J
i
k-
3
dG-
b =P.-o
a
- |
-5
-1
3
4
o
0f''^' I a
LO
(a-ll
 |
-/'- -d
+' --
/_r_
L
l-''-
riro
urf''Gy'"
Tt,4_-_: +l< /
l:_: --)
-l-l
a/.
/l&-:x
2. tL
t-71 2-31.'vt -3 1
3J o r o ltt
ol n-,, 1l1dl -5 1 1l
)
3 / a ro I
-lt
'' l-r L ! l
t-l-u1+l, '+la "J
o ..
11,-+ol
J--1 1
l-
rl 1 -
lo
y'a*Ki1. o A
1o
a -1
a0
o,t
aa
t'A
1€,Ao{-
-[
L-
*[
L
.,._l'I
tte
4
E
i
)
'-{-L//"J /.7
l! q l:l tl
-5 : //d I l-tlll 1 I |
^l4 4 )|"J >)
'/ /"(l r qt'I I l l, I | <-/
:l,t:l Y/ s=l sl
'l l-l' l-1 I
|) u- > L-o I
.
*---lntel .
{ 'l <--],-{ -11 sl
5 ll-1]'.{ 6l o l.
')
1t rl x'!=sc';-n',
I i f i
.:r: <r''- qr
-q I
--)
R'.,:e'-81
fr
).
.L
B
-f
?/
l-,)
*^io
.t
x-
-{.
9
-{
'f,
l
/:.
L-L
(= B
-S
j
<t
r^"ail-tl
t-
3
J
ax -{9 t3?
.,- ti} *.
,11
re , v'wJrrtrN_ lonnr
.o I t-
w,N-4
/it^F-l-
rnte
"t
!^ar^e+ €&qdl
-I-t
IL
r-,1, I n
l;
lo
14
6>r
o6
,+
jl
f r L {
-.
lo'* +
le e r
Lo 1 2-
..I'lo
Lo.
1
{5
4e
695
oo
v"
-
55 lKq
'"1 ,
:
tl
I-
sts-le- of !,;.<<tr- qx<Jjot,
<J
:),
v--l-
*=-2-
**o9o.s
A,K
-Ll lh< ((arl'Fo!e,
1'rrral
al a- frodrrct z+ -i1Jo
^{tv-
i,
-atA
*o 1L= lrcoBacL "{
+L*t'
i"-' tw',.t'+-L, o&(j
at'. n. B.: nY
Fx-or...llas (69r' t 4q'^ ? n'1 al - AFe-sa.n,r
(+l F,t t-e i.ew";<+a-of +r^e- di-e4"qr(€-
&. -rhen 4P-'= n-tn =I,,rl^enq f i'
on!
"r'-'
t*qHrx-
..airla€A ( goj'
#
iJ *J. o'&.a
c_-
+ "no-'i-sih*&^r(
Qsr - q14-
-ir^< uriL
a$*yr ".,--e;it,h,trLs
q, A
it t S
,.o1 On - ve'lOZ
.vr..,- sigr,i$a,--.
,'c$,
"-
"% d!U one  he"ap
a
't
. rt
.:l
I
I
F.
TT-< 4n.wrpcse- "L "' tnoA*.:t
ft-- Jo 1r.. e,,oA,,.t o! +oit
orl(qeR-.troof= fl.n-(
t_'"
bzr - -
NA,
d=tr'l--
of +..0
-,4',1r.-
1"
-lr@-.trrfos<, ln t'u*
te .lle
h
J
{
.)
.J
*l
-
_
!
^ertejor(g_
r +te
ilil
h.&^el ^T^TItH
KOa
sreg
I(o(n
-ft-F
ii'
t'$rok I
I
I
r
!':;o
I , =.|5 !J
-:
t-.J_,
'ili'
- it ' l; l
3f q .^f B qre *ro r.{ojce g".eL*.o*
,.--l-no
AB=f +heh A'-6 o..d-E=rr
A"(q-).---t-tlG)'=,
rl
q/t.dY
I N-')ts
-
fFl+ lY
' ..- -
'/: :l- I
- L.' -' ^.-.'f
- 4 I
-A
l
. ,/'/ - r
'i--1,,
- | r"q.Al .
a cr"4r+"(- I Cu...rt nt"O"s-
' h _6 r AlBr^ pct4^
r4lR )! - 3
$J n-]
A. -Then
t"..kix-
is, *i{e- nvcrs"- 4 +le
++-1
-41 ;r uinena
o,f Jr^e sa.^" oni.rt'
"n, s?lo'rre.,!"c;trix-
T i5 -tl^a t'v t
T} '
I A;i I
oq a+ 12-
Bl1 -
D
(r+$ +i5.
^nt{..oH
t+ +--L*:l
n- - .T
_ L4iil
lr'1
Ac'tnp.ir-ie-u1'e|(q ,, )=*l is
qne -t}'€ e"-'"c{on
A$- =,
t
"rh )
6l
-f.
, o "l
o i=*/ c I o - ol-r
I lt l-
D) la ao-rl
f tr o O -
-5lo ) q
l; i .
lo oa
Slwr.V{fd-l ) k)e colrr
.Th,,4
f tl-'
*l^otn +t-",$ A
tA
-- 1
=A-+= I
]! * ra.lti 1- 1^q-o,^',n,erasi+ aA a'"lg rt il
iS 16q- sir3u$oq ,4 no"'-s$''1''r- q' nw{rtjx- l"a
o -g- ae ln€/rre-.
q-u[ ?
suppose{u$ * i 5 a} +i^€' .lh€ -U?e
*xn *^!- aros.
*-f ." '4: A *
n1,,n .
,' inrerse4:.,ihe
^
*"t;n
Oft*rff^
"fu
ar(€ batl^ J+ n"&
*'& d L
-
rc,
ta h@
^ -- -
4-t A ""' rtrh F'
,iB = -ln_ c''
E 4ln 4T L [L - SiYea
c^rcl
'n q +1.< Re^K ,I 'iL< PFad&Q't a+ tqlo
r oR ^-,r{ *. i]^e rro- K.f-o{rr.r }( ls qq 'l^dh
f .r, n
ei eJTlFrc +q J'-.
'n
He-rc m= nr K a.J A ls ro71 si8uroK
' '' r
3i Tr4.'rro fl€ a.ot"&! $!'l'0" s si'ht-xc'RtL
'
trar.g.- 46-t= I-.
url
I rh,rh = r 'n{F /
r..,, L_, ;:
. .
,
.:
,. _ i
.
NoLr.suf,pase .tfd. A = To.iil Is ridl.-s1'8l^|€r
'' ' L .-".!
si-,ee,A)+0 , 6€ c^,r J"F lti =
H3
f t,j--,... -1.
L
trl^en,- . Ai; c(e *re c" -Sel.rs
^f
oii in fi '
-^.rui,. "'J
' $ ' r' f fiil . -the?'lcr. g k {le r"YrRlX L :J
- rI ^.. , .1 rl ","]-rdl=[.rfl_s.j,1s,i-AB= la "'K b'1/=/z-c-'KG--i-l1Ar-""1{l^. !r,'l'' - lH.' 'J l"l .r
itii-r,;=l.l
l
'.:'
sil-].hr-b sc|,
s,h</ 3ls o.-" i^'..*t, af n o"J ele'-4
- ,0 '., n l^aa a- i^ lt{'ah<+
1^sn.s'gulqt ne,-trl ,'
I
+ te- k".*e }o
"n-". si-1r-Un
o
+F.* s.3
/t t'
r.ve'.+q - ?&
-Tt!<y ut€-
shr" iut,la in'ie"x' e-f 1
w.]flry. n tt^i?€ ' s uf,Pose-
r r. -,dl
"c.
-.'8&.f o'J- A- o.
g i. ^iLt
o- Y'.t{-
o} ar'
l-"*€- P'E=I'
^ . *Lrg eyJiarr ar 14
r^tp).1 e".Cl s ldl€
'c-
tJL t.4 g -  . {t en c':e 5n
d
i
II
I
I
F- P,-
t. , r^i" 1(]" ril7 .'i
aJlfftco ulra{-
Q9. oS..'tL
Ro',,t<d -"lnjl
;
f6o,n
*liis ce,ae
rnn{n'rx-
A
"-&
is
en it^<
MLe(
ffn
rq(n
A ls
^ - Krooe& "1"oa6e ".{tin C
i, rof=o-$-
{""d{r'r !( -fe-
lo.a G4.f.k 16: ',
-tt^"n oalle$- o- 'ro's'!eL'}.fr
?,.A{d.x-'
"".!+ +F+o
a{I"$.
,^g il
sir-plor-c
a
il -8
r@r:l( G o| Jt'e r'"{tdx +
"t
r.r^- 2€@ lloos
O )e+q!Y^ina -ti.e *o-r' "l
r'.trrr( A
L
-11
.l
,l
;l
I
ls -ll'-e
"o{r.i^
+
'51e.
rA 1
,Qs-l r a
I
:
Ll tr
cd€ Re
1l
;l
Qt+
4
I-l- I ''L
c
3
'{
6
'j
':
-3 I
'r j I_.1 I
_"
*& I
(0'-
n,.
-2
-a
-.f
I
d 6-
oc)
oo
1-
T
I
:1
'1
a
a
0
a
o
o
0
^I
k'K o+ w*l{id = B .
-Tt<
,1
l
--+,' :-
-{
-5
o'
a,
-r
'?.
o
q"<t q
{-6, .-&-
-{'= d -&s.
-C'=rR'- gr '1
ix+et<V€"y4 -
-t
r-I
o
^l
-s -1 |)
I tr,
I
+ I r _.(
l-
1 I z" R -1
^ =/' -Z -+
-r o- 1i '+
t- - {
.1
-.1
o
o
I
l-
a
o
o
o
1
o
0
o
0
o -.- r ',2
)
r T-'.K ,9 **{ni"- = f
'1x, -h.en
{.,'=q,,ar. -:.ra""ll$<
i€
forc sooae so'ler ?' --re <atetr
'-
l< a'fu'€&
o..^. 616en""[^e- "$ "
it ' 6 soi& *#*
e- -ieen'eer '$ +'aoni*zedYdi%f' y
4W"
-o{,-
rrt yJ -- A
,
t:'Lerr< -T '
i s ad 'nv
]ae+i+.1'^-lni,<9 '/ rs
i ,""T*f
ls *t* TL€- ou'no'"ewlte r"^<$'r< o+
J
l*. ,*F,.*l*6Ltd +t"q
I
ot^-r,oeJe*+e ?.+.i^ ol ;', -ru - p ls c.
' ', ijrr.. ;!'"i,.- r;-,
f.!6""r" q^[ is ? g i. .1'ttJ +". et.nae],ts]lc
er,',*,"(.J *l:;
",^*t,i"ttt*1.,*,,trA1e€r.rs" . -,,-kn^
es*."dr. 1$J...::,,
**"ki
I
I
I
."
!. ll
s oa{(ecl tia<
. l+q< sii<rt,:
,l- n- or^t(o-e{ecs$. €4J4SSo/
I a, r, -
.:r,
..r
a'. Icqq vgertc..
7= 9i *..,,- , .lL
I
I
T
n
p$4rvr"r"J .t'
.aY"dio .t-r -t-- "
)"41,
o-
1,f
'r
t_^AI= Iu
')| Q -:9 o =9r''"; ' " ''-''
-,'r-
.;Q"-9u=a '' ,i-..
,1 --. Li e,"e..r,e&+e.5h" .
d5, a9 !a-
c?E - )tl
L ol
^".1U'J
vec,FrL
&rLley* 3
ir,Q
--'{..'
4lae eigcn rnalg^e
all elge'dl,{e
e Yha1trtt(-
_ .A
' '',>+.:.,,.':.
dl^q Q5tfr'.'*='
Tq- s: I
'...01-+
| -r'
L-:
-.:
.J.
&
.lr
aTnl
Fi'
+
1.
# i..
, 4.=7-t-+
I f "
<
I ,--,1o-'.^) :. La -s
r€ et
'{leefec6h e *+nlt , 4
l-r o t
1dl
- / | a t'e
|o ? i
"4"-
-t=
IL.J
t
I
!
f
{
{
t
.i
r.y- ,i..-
- - ^q c I
"v.cJer.gF c
q)'j4t1v'' -
'r1 -r;o
-r|"<
L"S,1€
=lr'- nl
;)
-s= (l- t )1U>n"t; (',:-t) . "  I *l('- :*"
- -'l' ' '1^--F-I-t rj"o <a^+5/.
- /r-i l'r- 1)l % L)
- ' //
! //
"/
td "fke
l+x
i ^. .1(? Ll (rrL)'o
, r-7' -' '
- *- 1 ,2, D'-
. [='
*l
€i?e^.6eto(r := I ;".,l -****g
r o."g "l "^!a3e^..et$n w,Lre ? r+
- ^ 1.^ ,"1Ut -9x="
aa rwn -lnivia-[ s'4u"
a
L:ie r.,I
gq..
-l
=[
- 12 +^J
5{.i-- "J
Sslo""' "I
a
o
a
:& (.
4in er.G
x,_t-
f,J=)ol
.^ra
LeJ- +1"e"
"al^e cj.  -- c"a +9 .
rr.< e-laer,ve<il0n d 6 o.$rtro6ai"Si? -lo +e
7r ze(i, v<rftRr oJ€-lfrwsuq, 1e= I .^---' lal. I r - |
{r€ -1!Itr"1 o
I
L o)
--, ,!-' x"h'+-tq .-
z- .=0t..
l -.e-t.L tar"4_ aaet.anic.lotq
{" -c f4.+;)2 'J-'- t/L4,L
[ +.'' * z_ tfrJ'; 1"..'
I o l-).1
I s -qe I lol
)
^)
t*-t^ert T---.-^.Ar!^"b."e^ g.}i' ;'' ."-i''
f-: ?- r-l fx, 'l 1"1
Lz i z)l:t)=lt). :'
-1
.!r,rec-yt equ&rr -:x1 - 1r<zl-! : o
gtr-- 1 -
d
Jr.""'.-i"$<|:e t^4€_
*
-9a-
1r'<e+o cnil p"t8 + {<."9o"
le! 2=t^a1o) t'+
o
T-t,-'alsi
-
rt -_ -4
t
l') *' '' '+
l?-:*'=
nr-s"
L --) -j = i1:
1
__ : = .2"-
" r , .-,^--o-vr'&"E l' lk'
-lfa eage.rxcL'R :f -
*''."'- d
-<"'^
lutt.a.-.. + T' 'u ^"
Y1@^k*d
. | -. f n/' i
r..{"*1 oi 'iq +o-, x =
I 'a.V"l
.l
L1 -1
L t"l
t" rc,r,.e"Lq,.-_.1 .fle. t'.--
li | ''
1ts1.,e -- -')

More Related Content

What's hot

ITIL Advanced: Phase 2 (Service Design): Service Availability Management-(Com...
ITIL Advanced: Phase 2 (Service Design): Service Availability Management-(Com...ITIL Advanced: Phase 2 (Service Design): Service Availability Management-(Com...
ITIL Advanced: Phase 2 (Service Design): Service Availability Management-(Com...Chakameh Mortezania
 
Ee made by mrp
Ee made by mrpEe made by mrp
Ee made by mrpjibonghosh
 
الاسماء المقبولين في قسم الادارة القانونية للعام الدراسي 2015 2016
الاسماء المقبولين في قسم الادارة القانونية للعام الدراسي 2015 2016الاسماء المقبولين في قسم الادارة القانونية للعام الدراسي 2015 2016
الاسماء المقبولين في قسم الادارة القانونية للعام الدراسي 2015 2016Techkirkuk Kirkuktcweb
 
انسان و حيوان صداق هدایت
انسان و حيوان  صداق هدایتانسان و حيوان  صداق هدایت
انسان و حيوان صداق هدایتFarid Kamali
 
skin biomechanic
skin biomechanicskin biomechanic
skin biomechanicsarashoghi
 
Modern Power Electronics Notes on Resonant Inverters by P.Praveen Kumar,Asst ...
Modern Power Electronics Notes on Resonant Inverters by P.Praveen Kumar,Asst ...Modern Power Electronics Notes on Resonant Inverters by P.Praveen Kumar,Asst ...
Modern Power Electronics Notes on Resonant Inverters by P.Praveen Kumar,Asst ...Praveen Kumar
 
Biomedical Circuits & Networks - Network synthesis and filter design
Biomedical Circuits & Networks - Network synthesis and filter designBiomedical Circuits & Networks - Network synthesis and filter design
Biomedical Circuits & Networks - Network synthesis and filter designMathankumar S
 
Biomedical Circuits & Networks - Transient Analysis and Two Port Networks
Biomedical Circuits & Networks - Transient Analysis and Two Port NetworksBiomedical Circuits & Networks - Transient Analysis and Two Port Networks
Biomedical Circuits & Networks - Transient Analysis and Two Port NetworksMathankumar S
 
Nuestro Recetario
Nuestro RecetarioNuestro Recetario
Nuestro RecetarioRaficora
 
Baba Sahiba (Ashfaq Ahmad) BY meritehreer and My Publications
Baba Sahiba (Ashfaq Ahmad) BY meritehreer and My PublicationsBaba Sahiba (Ashfaq Ahmad) BY meritehreer and My Publications
Baba Sahiba (Ashfaq Ahmad) BY meritehreer and My PublicationsMyWritings
 

What's hot (20)

ITIL Advanced: Phase 2 (Service Design): Service Availability Management-(Com...
ITIL Advanced: Phase 2 (Service Design): Service Availability Management-(Com...ITIL Advanced: Phase 2 (Service Design): Service Availability Management-(Com...
ITIL Advanced: Phase 2 (Service Design): Service Availability Management-(Com...
 
Discrete control
Discrete controlDiscrete control
Discrete control
 
Ee made by mrp
Ee made by mrpEe made by mrp
Ee made by mrp
 
702 stories
702 stories702 stories
702 stories
 
حلول كتاب الوزارة (احتكاك + تطبيقات بيوتن)
حلول كتاب الوزارة (احتكاك + تطبيقات بيوتن)حلول كتاب الوزارة (احتكاك + تطبيقات بيوتن)
حلول كتاب الوزارة (احتكاك + تطبيقات بيوتن)
 
Physics c hapters 1 5
Physics c hapters 1 5Physics c hapters 1 5
Physics c hapters 1 5
 
Chps. 6 10 physics
Chps. 6 10 physicsChps. 6 10 physics
Chps. 6 10 physics
 
apt hope 1982
apt hope 1982apt hope 1982
apt hope 1982
 
الاسماء المقبولين في قسم الادارة القانونية للعام الدراسي 2015 2016
الاسماء المقبولين في قسم الادارة القانونية للعام الدراسي 2015 2016الاسماء المقبولين في قسم الادارة القانونية للعام الدراسي 2015 2016
الاسماء المقبولين في قسم الادارة القانونية للعام الدراسي 2015 2016
 
انسان و حيوان صداق هدایت
انسان و حيوان  صداق هدایتانسان و حيوان  صداق هدایت
انسان و حيوان صداق هدایت
 
skin biomechanic
skin biomechanicskin biomechanic
skin biomechanic
 
Modern Power Electronics Notes on Resonant Inverters by P.Praveen Kumar,Asst ...
Modern Power Electronics Notes on Resonant Inverters by P.Praveen Kumar,Asst ...Modern Power Electronics Notes on Resonant Inverters by P.Praveen Kumar,Asst ...
Modern Power Electronics Notes on Resonant Inverters by P.Praveen Kumar,Asst ...
 
Biomedical Circuits & Networks - Network synthesis and filter design
Biomedical Circuits & Networks - Network synthesis and filter designBiomedical Circuits & Networks - Network synthesis and filter design
Biomedical Circuits & Networks - Network synthesis and filter design
 
Khutbae fadak
Khutbae fadakKhutbae fadak
Khutbae fadak
 
Ijazul Masih Urdu
Ijazul Masih UrduIjazul Masih Urdu
Ijazul Masih Urdu
 
Biomedical Circuits & Networks - Transient Analysis and Two Port Networks
Biomedical Circuits & Networks - Transient Analysis and Two Port NetworksBiomedical Circuits & Networks - Transient Analysis and Two Port Networks
Biomedical Circuits & Networks - Transient Analysis and Two Port Networks
 
Bab 2
Bab 2Bab 2
Bab 2
 
Nuestro Recetario
Nuestro RecetarioNuestro Recetario
Nuestro Recetario
 
Baba Sahiba (Ashfaq Ahmad) BY meritehreer and My Publications
Baba Sahiba (Ashfaq Ahmad) BY meritehreer and My PublicationsBaba Sahiba (Ashfaq Ahmad) BY meritehreer and My Publications
Baba Sahiba (Ashfaq Ahmad) BY meritehreer and My Publications
 
Ghadeer07 08-09of11
Ghadeer07 08-09of11Ghadeer07 08-09of11
Ghadeer07 08-09of11
 

More from foyezcse

Tahsan bangla-song-lyrics
Tahsan bangla-song-lyricsTahsan bangla-song-lyrics
Tahsan bangla-song-lyricsfoyezcse
 
Laplace transfrom lec
Laplace transfrom lecLaplace transfrom lec
Laplace transfrom lecfoyezcse
 
Math for cse.question
Math for cse.questionMath for cse.question
Math for cse.questionfoyezcse
 
statistics
statisticsstatistics
statisticsfoyezcse
 

More from foyezcse (8)

Tahsan bangla-song-lyrics
Tahsan bangla-song-lyricsTahsan bangla-song-lyrics
Tahsan bangla-song-lyrics
 
Vector 2
Vector 2Vector 2
Vector 2
 
Vector 1
Vector 1Vector 1
Vector 1
 
Matrix 1
Matrix 1Matrix 1
Matrix 1
 
Fourier
FourierFourier
Fourier
 
Laplace transfrom lec
Laplace transfrom lecLaplace transfrom lec
Laplace transfrom lec
 
Math for cse.question
Math for cse.questionMath for cse.question
Math for cse.question
 
statistics
statisticsstatistics
statistics
 

Recently uploaded

TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...Nguyen Thanh Tu Collection
 
Seth-Godin-–-Tribus-PDFDrive-.pdf en espaoñ
Seth-Godin-–-Tribus-PDFDrive-.pdf en espaoñSeth-Godin-–-Tribus-PDFDrive-.pdf en espaoñ
Seth-Godin-–-Tribus-PDFDrive-.pdf en espaoñcarrenoelio8
 
30 ĐỀ PHÁT TRIỂN THEO CẤU TRÚC ĐỀ MINH HỌA BGD NGÀY 22-3-2024 KỲ THI TỐT NGHI...
30 ĐỀ PHÁT TRIỂN THEO CẤU TRÚC ĐỀ MINH HỌA BGD NGÀY 22-3-2024 KỲ THI TỐT NGHI...30 ĐỀ PHÁT TRIỂN THEO CẤU TRÚC ĐỀ MINH HỌA BGD NGÀY 22-3-2024 KỲ THI TỐT NGHI...
30 ĐỀ PHÁT TRIỂN THEO CẤU TRÚC ĐỀ MINH HỌA BGD NGÀY 22-3-2024 KỲ THI TỐT NGHI...Nguyen Thanh Tu Collection
 
French Revolution (फ्रेंच राज्यक्रांती)
French Revolution  (फ्रेंच राज्यक्रांती)French Revolution  (फ्रेंच राज्यक्रांती)
French Revolution (फ्रेंच राज्यक्रांती)Shankar Aware
 
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...Nguyen Thanh Tu Collection
 

Recently uploaded (6)

TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
TUYỂN TẬP 20 ĐỀ THI KHẢO SÁT HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2020 (CÓ Đ...
 
Seth-Godin-–-Tribus-PDFDrive-.pdf en espaoñ
Seth-Godin-–-Tribus-PDFDrive-.pdf en espaoñSeth-Godin-–-Tribus-PDFDrive-.pdf en espaoñ
Seth-Godin-–-Tribus-PDFDrive-.pdf en espaoñ
 
30 ĐỀ PHÁT TRIỂN THEO CẤU TRÚC ĐỀ MINH HỌA BGD NGÀY 22-3-2024 KỲ THI TỐT NGHI...
30 ĐỀ PHÁT TRIỂN THEO CẤU TRÚC ĐỀ MINH HỌA BGD NGÀY 22-3-2024 KỲ THI TỐT NGHI...30 ĐỀ PHÁT TRIỂN THEO CẤU TRÚC ĐỀ MINH HỌA BGD NGÀY 22-3-2024 KỲ THI TỐT NGHI...
30 ĐỀ PHÁT TRIỂN THEO CẤU TRÚC ĐỀ MINH HỌA BGD NGÀY 22-3-2024 KỲ THI TỐT NGHI...
 
French Revolution (फ्रेंच राज्यक्रांती)
French Revolution  (फ्रेंच राज्यक्रांती)French Revolution  (फ्रेंच राज्यक्रांती)
French Revolution (फ्रेंच राज्यक्रांती)
 
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
TUYỂN TẬP 25 ĐỀ THI HỌC SINH GIỎI MÔN TIẾNG ANH LỚP 6 NĂM 2023 CÓ ĐÁP ÁN (SƯU...
 
LAR MARIA MÃE DE ÁFRICA .
LAR MARIA MÃE DE ÁFRICA                 .LAR MARIA MÃE DE ÁFRICA                 .
LAR MARIA MÃE DE ÁFRICA .
 

Matrix 2

  • 1. ,2 -mEegx l rfere&ev @ ln/r'.rte doum o- mob,i< in lla gala:."1 b.t n . Ed; t "t L6 con4;dat, o- ze.t 9b inutloi,zoqa - eq,"ttipn , t +2y +32 15t -o +L -rzy+gz+7* i o !t- +4y +u2 a g2 , 6 Now, we wlile down Lh.e otr jt"4 d.6aveeL,,.tiory "::::;f;;: ^11;.,br"akel^ qrd. lhzn wq Be*" n=f t 2 z E1 l+ z i '' Lt i 2 il 12, ab'1e sy,tern o,l- ,rarnbeyA - anq1gpd ) n a"-retto.n}l/an ),rl,owt qtt| eolum,t and. bo4la{ ty Lh-z brqehel,,, jj, callpd- + no7-rt. An mo,l."ix b Wz"l m.^ ,_r"*.n ^, t%,"L,tt- ^-ly't:
  • 2. !.9!^yt:2) Any 1xn ^,nalr),twt;< hot o y orL. -+ -r.ow qYld n eoju-m'v, ). e "A-al R+ row n"inir . L6-.j a, . ,.. . arj Et A=lJ t zl -t /n _Lt3 _. COtirm.r -tn<,,trtxI A..!------'----^!,--'^ ftny 'nLtmbeY' o,k t:ov,tx Et , A,.l t] . l:l. ,3xL 3 Or-thca-or.a{ -Jri xI 4 -,-t_^,1^ ar a'.lhcyona T^o'Lr"' /l crr J. t]1 )-r"r'tlozz rlr oJ-.irz A,A,.. '"8wt=a -"aL'r,,t h0, l' + oqe q4lwn a .:, 1d p eolk d q col-,,-, ).Ltr.. -r.rqqre tq-trl,< A "tr, t-Wa" ,6 )4P prci,J ob o, ,",, , t1otr)x A' it on. ilzrl;"ty +. !,rof e l",Jrir ; .-;=^-T-_noWA 2A eq-i{o, -gctko.ne Toopt( , A 'no,tli r. in wlrrch f,hz number o1- o& Al .'n 11 r- otri r-, F-N,'. A - !o Lhr nu-ben sb " Iurntv5 i,. '",/14d ^ra "*r, re T. 3f ul ro3 w }.iel" ra = r A <Jizd zaat<
  • 3. 9-rne,y b) l2 y,$3{t{i -Iwo vnol-pk<zv,a're .',d'd t'a be :l RXtJ{g< 1l'z- rn,1n mqTot ^Jho;,eekt "t.tzole o.l-{ 2<Ta iL cquLd_ L.e nu!_I.-DJ'nt", F't'. x=1'oo1 P ol_ ) 2.r,L I n."*-r"t Ynatnia:a ".,,^-...,. - molr"r,c ,+ "rtWa q- d;ayrnJ t"oF., L . Lb o"U ,) "." . tW""^ eb,"ert' .ire 24 to oR,, %'fr"i- B,i i*', oit'e ok Ih4 el4n4L }i Lhr. Adr,e oyd4r, ar oir,< ,tn I corretpahdlA- por,ili*. ane -5Xacr.enatr.ir )> cqu4d L,r*o'dl el,sJw,.L a're +,.ly 6,i2 zef a , b"" r-.'.n[r z] B-,lL trq p A -cq"o'e -"j"'' A 'La,il - ho',2 elo.".zn)+ qDove anq 11,'i.,r*,0"'*^ e";",i *, a),!z<ro ; <altz^u^2.an lholr; < t.: 4. [r o ] , St., ol Lo*1,, LS L i|ur., 8.Uni.t on Sd{nl"ly -olni,. i A r--,----^--_-----l- _ - a utrrt )"n#'.ir. $ oll ult o.nL -no, &a3""""1 elZrufrA bbk, A dl'cX^orar colta.{ o.n -o;.i1l d,ia;,ona.l idan*,i.*>n"ir'x ' e.!zr"xrt^ q-rg o)1 onz i+
  • 4. Et" 9. Sca-(el .',aLt'* i Z--!2-'-'-2------2-'.! a:pe aU e.y Lcul-b Lt- . A = | eL La h d:"go-"l al1z.d a, ,"olfix k"1p"J -gcqlqr, zo.*rjz. Ir o o1 A-,lo 7 o I ln o 1 | L" -) ilrrr oJ1 trpper it)en4llla 'h;LY))' pr;n<rp"-[ &ayanJ dr e 24-ro . A=lt z v-l lo z t 1 loo +l " ^3^3 eter.ab, -5xq^re; .r,J''i,,L ,9--Lo-;;7 & tlra d4nain L<lavti^ f},r' Et-, LL L'o'.Ler/:t)n,gaar toty.ix : A >tTo.qie n at.'",t A = W* a& *hP el4i'''znt' lt z ptit dpo! d'aynJ ate z-zt"<> aool LTal 3 4 +)txs C qJ O y4rr-'tu ' r. ps Qruh4]? t f Yia-,ti . , ..ll tz .ASym 'rnetT.i' mN 't , A )'4u e maLI) * """- a Q{16:,ymnoltj c..Det€rnih-}e ar vxli | : be c&lPA 81,. A - /a- -l 4bove /- --------',-'1--an ^'n"i,JX -+ -b"--"ij -v tr"' a)' i at'f, 1 a, i 0t, k'= A ' lr wfPQY
  • 5. 7 aR, A ^Iaqve --^L-ti/'h+A=s-L"ri A Aqtd i.o E<6e -:r-y:,". t .ij- ( ,. i), cle -_ nt i* tiz +an< l, ^r,.,t el,evvalgs.s,, "l ,, ..or, bT o-14 Et' a, Li Ske't sym-ujri< :"no,l,-rix'A >r+,+re ,natt; * t+ , nAted /..-''----....-/-'--"....--^-^ 9l1ew-.symp2trie To|aix , )L ,) nri- . nj; |,"r Jl "Ltue; .E 1 &4 ot A'- - A h) Atl.l,qo"*|" o-lzn"znl.^, a."<. z,1.,vo. OR ah3,1 h b,f / 9 { cl
  • 6. i :1",[r o o 1 ln 6u I lzi+ | L 'Jt'9 L.-f. u.a. t!,Sit'.X."ctor "- q,tri'. I ,'!--!-^'^-,. 'fo,.tirb< j* 24ra '4'14:n :ltng:tbv 'r" otatt< At' g"r 1Al =l L 2J ' L3 4)zrt LC,I'qpo6z ob 'motr'r,, i q* /./.-'J.-.'.---'',,. ll,terrhon;< *l'e row,s qd *U 3|. *hz dal€th)h an* ok :LM lv"e. n*bi x "b l,nown )a ,tb L-L --o l:he].^h b' a Sing"J* roJr.4-t, L ttv<h '-.^|]i.)< A, 4Q ea'fie, pordjrly eo,l.Qr,n4 xhz- 'Mw a)'- khz t-'atr)t .L.E^nzd ) c ^.!-trpd, fW:- *vatapaqe '(naf.rr t , i/. ^ d4ndte| by At , b or<. ue, A, F-*| A --lurjl -^n th-eu "tV L11r ^ma*tix aLlivd A by evung.iny*s tart ;t;fo columa an) colu',tt4 )lnto ttt z i* ."U'zd *hz l."apo""< o,E t 3 ,', A' or' A1 -- 17. Uni1".ry r)o"tr)t ', 4 /'_---'^------ A ,,,t -.ta'd tp b€. |.tll*o.Py- ,l Ae4 ^[: lr . e1 l3 o 7 | | + 5 3l L 's'= j o 7 .tr<Lu!.r'e =fi.L" i,
  • 7. -:I l -l-j -t L+' oli o 1loytna) A qnl 1i€ tl. aR*ho2r:na.!" +.-rtaUpaS.e ,1aL"-L/ ',^t-it ,jtr: ". AA'- Ata --I JLr tAt: ) ; "-,oJtt t- AL ?rop?P Lt. Ccr:lcratz ah- tno,t:.ix .. LJ "-.,-----' -.- -.-/-/_ ^ 0 | (. c ^t]_e ot ca^7ag^Jer, a ot -aF ^h..L atz-r. cL ' -L: a +iri {rnDte4 b t j-;';r < La bt ^ L oF 'mo'trit" Erarpk, W., ^-1, car,i4FJ:z o.I, tJnx fiA F -1 I Lhz 'rYrdLrrtrL A Pl,odLlcl, a,E a c a.!,lzd ),, "1:.1y r,rrte.r '1 i, )zf .:,^lI 1",?n 7, q1-j t eo,npi,ott number . -6* cc,mplax :"omi<-rn o-+6i and c_6j, o- alrd b re-{ I'un, tU", cor)4qyatc *d ;b, """iul. ) . ).t1,t c..lkd cagwg^t< :,,1 :,,1l].;,
  • 8. ZCt.Hez,r.tl:;a.n ^n,*r)x : --__----__,- rl =la^rl .ruc t"1 A h HaFm&q., -$gL{are r,d-tr-t>c 4 6 <"J!<{ A ;, Her"r"";;L valuz4 ",& i and l', DA ar 9i€*- ha.nrnitiqvr p l, A tl,tare lna*i tc 4 h4r o.l-i,tj "", -^"1.111 ,)y a. - : a. hot' o-!) a7 At rth2 k,.yon"- elzraaala q).e. reo-t nqmber). cotl,lt tz ?ro dzd Ci-zar)" OR, ,4 *q.u."a r1;lr; t A.lct,)) La e ^!!zd h4".j-fur'. -J,it i, Qve?y- ',-i t e!,,n"^J ab n i^, ey"! b (a.j,a4e ap^pbr'. 4- i th oE 4 , 9t,otlt v a.p!)-*,, __u-,ltiti; t;_,, :.: r N..tgo,y ", d- ...tt.o- ^}1 ""^*L1ti)Ait'" t:'J,, ", 1e 6e Het'niLiqn -i) ,{-qJ 4 , oU on Xr^Apo),< o,e. 4, 4"-U)' 2L 9kew - l,,zom)j)qo mol'nix l -tLu"qi< -.,q|. t |._LiL,, A Aqe *rot. At - - ft t colkd *kew, hq, hqn . -hc,-t 4 * 4vew' h.e:rmi'ti">tprovikL 6,;4 -..; br col,XvJuzt dr .L and- i. Cko'ty , th,z kq*ohd1 el<vznlt, o/- o,. We.t - hzrh+k^t1 t,r_fi,.rz o^< ',to-(iN)c, ' Q)+t'n' -4ra-5 oY Ptrt'e '. to,, , - ))) b< . ql.!r), o- 3fr r')) <!-1y t_ 7 fl1 eb rrr,t b A 2
  • 9. -I :_""-t tu w tul)uz e">,)ug^te ( ov'.,pb,La.!, F t, '' +,, <Izr"<",h "). /] . i " o*rtan vrorl4: q,, =, t., 4j _ii A lit nL- itL4 .,1o,,u,+/t ,n ) vLe _". o b t.Lt t. a. h . r' uP'L d'oytnJ ^ LU a-'-."i) - - q..i at, d.. + a. - d - an-qa,b ),*" : d;..,= x ^b .(cr+)b ) tLq ,b) _/) ;, Zq =o a,.6 J pq'fe. ^- agnqr.y O.t" aU JaW &.aq1:lna.!.etznwlz ,ne- eLtzr za.jaa a.r pqr e, *t 2- 3; o 2; 5e o o- Atlea het ., tL i^ajljt11)a t"7 4z-4 9o f{ovt 'lJ,.r ":?'l -3t ,l ' A -+ucb n ))1a f;t^. I ( Zr3^ t' L- Lf-t) ) Lu 1dzmpot<tdt o:fu).*. 1-_/--__,--,__-- _.,'-_____-_ ^ )o 6Wl, 9dtnpot"t* ".^ttOl{rEt'. A,f , z -y1 /1 3 tl lr -z -3 I ^-- lz -t +1 "-l: j +l t' -L -3 I =n : .,1
  • 10. 2l -I''lcom-l .l.o,1f {( . fi.z syi*q /_.'/-_----- /=^ oA- nttynLer^ dT]c|x,€d- -.i q t<6to1"olz{qr eo^Lr-n, o'rA L.ullzd by ro?Yhql ]^qtrix, 6 I 2*, 9nverl4,^ o.l- o_ :'t,-Lr) x I g,L- lr.to .md: ee-t, A .,t dB/_-___--__,--- ___, ____, ___,_^ oa?e Lwo .>"6an'e, tn ql1.r.z^ o), th< -XdnL4 ord!j,, Lrch L,* g.ttt ra.i!-et *.V,2 )r,er4oz A cnd n A /h< vucta4 ol- B, E/'. B-,A'r, whzte AB= BA=I, 2j s."uJop rno,Ir"4' 41- thc .td?t,,"vaal oE L*:- na|n. iz zala, Lhak LLL nvLtit .i-', no".'1 ax -inytlar v,a.t t , E,(. I AI=IL 2f = L- e =a r l,a! 4 "z a- ingul+, talr)c,er,, 13 el .2f-Ncn- a,"ya!ao r"Je',r:9t J2 S2/z'tru-)e ..---_-----,.-{,-,-''r.----'.--^'-J,il ^io| z-'e"co,*hzn ht'z'r"J 't -rz q'fr1.dy )n ^Pou/^ 'L *h2 oro<he 4 ./Lt qxd, c".!tkA i),, Nayr,*"'r5.rl,tor -r,,J"iz . rt'. lAl{a ,lhzn A A a- Na1- 44*utot hdtD tz). non- in4oz be i*;-> . afun a 51r.ore-mati* n"t )nv ,^. -,-'--.-,-' ---^---------'ry A snytat'< ''habiL" A' *o Va4^/,A dn inver^z- j4 1r3 "n1*kix A A , J)t ^ n" a o- 4nLL6re 1. d-ti/- a,, d. ,6g a e'r// , kvu"' 4g -- I A: L ,
  • 11. a?ro.e r...1r-ra YncLLn)ce a$/ t)< aE 4 an" 4 p L"* t /-/rrRrcEs / . ^ /*^^- l;::*::"*:-* noLo,n whzn a. C '4, - <9L< , t- / qnqg o.ne l_o q,ope ::Ytz otdeP ' Ntch LhoL, ae=u,-t L^en B 42> c o-trlza 1^-e f,z l,n,t<n* ok B a4 n =g) .n'eY+e fi.ve4 lLr o ltore rnolp' /, 4 ,A rta.t- unNop lfrl*o. i:se", ^tuq)"e.moirix Ata poN4-eg )'l e42 tg.3h A_lr -t 6l " - l" -t " f t-0.o't Yzo"sl Lt o ol Lh'*, ,l=[r -1 o1 Jz -' o/ L7 a al _x -1 o/ lL I al ,l L.r a a-l = I(o- o) + ) ta- G)=o dzt'LA) o1- o 1c t-J) ' d?a
  • 12. Co- ,F,',e.tot ok ArB 2 l -l-a o a a L lo :l A", 'L a 'L -f -1. La+J) Io*J (-r1 1 I" . t1 o1l a t ol :T O 62- l l;,l-1 01 - l-r o oO o io-1* q.-(o*) lo , :'l = 0 -b -t I lat sz | | ^/ ' AqtA)=v') '- :l I F, 1l ;l [o o - J o-t LL "L
  • 13. i"". r+*+ LyB)l . grp, .whpnA o^dB arc rarik kdJ mt M),p,tt,ol;on- oR_ no-.)-inq,.Jq h,rrirog 3b A o-rtd"B et"e. coraPqFohlz '"vtr;e,+ andA" oqd B qlaA Lh,z tt'+Upo42 ma1 .z- o E A a nd B ,15-,r' w hare It ?; be o.n b< qn mc-L t AT 1;,4 ) ai)-12' c. h. Ye,V"tlive)y, ft,lzn pooveth"I, @{= n'B- Lza] J), A md B qr< Lluz t-wo tJ ee+ eo,,b"vnA y'6duxt nB, i: h'en ,1how *hJ (he) =s'a' "a " v4 'oePre;"er1lz*oo4p4tn r a- ,nait')x - /2 B-- b,, 9;,ntz, pB h *, *rp rnJ.r^r. 6a e1- -t a p xh tnotr) r . 6ur[htzr BT b gx.' moir)r. and r-ol,rr)(. l-heretol " , B,n, ^fruo , (0a)' ond grsr ^rr""--';:Na-, {V 1-.1.;44 e.!2,,,,^t de.,zrt, o,t: (nei _ i" ^ 6 = ?' o" ^oio AXAa) 'fi.4 4,L T aa J, c' 1,*hz i,t colr,,r 'r ah T X>. "? /)o,1ae a?d?, ".-,bi, tAB) -
  • 14. Flg,ol'r @ ard @ ,we have (i, d, UBf --U,i),Lr, <1Lzwzntdr At, /hLz v o,tix LABf ,tnd B'Ar A I de" o.rd .l M" (orret,lafla;4y c:!pr,.-_L equ ol 9o, (/+B ryg), 4 an ve *ht T /-tr_1 -v ) (nB) ' dBar. | ^^ -lrHb) - B n f Zoo;,) 13n-". ->'tnyt'-hr r*,o (n'') b-a-lk ;k ;) t',h elznzxt Btnt, qne tz A az.€ a>e n^r) 1ea2) , -2 '4 AnA erJ '.4 t-- - i (AB)B-'I A-L^J , t3fto'11n-r '- (A,j).At LBe-"-t =L )t-, B'n'- fpro v kno* (nn,t P1oo fn') 9al' ' *hd'L ( B-ra-r ) te
  • 15. ho, B-LA ''(ns)= a-'yn-t1nesJ - B-'l(A*t+)Bf =;r0,0 . B-'B =1 Jd;,^k"" ",&-L/nveLL< o)- Be' - By Lhe za6,ttrx, B ' A-L .i.t- ), r* .)_ , s ,'' (ne;t: s-Lo-t f PPoveeJ -J u)',4, ah?re lA-'))-lrtt) .lP 4 {a co?cf ', t -lo) | suet,Jl^dni3=L ,- / 't:tar, 4= g-t =t i oe]_-q t_T r.JocJ. tr Lr f aee) I n') =H ' €..uq
  • 16. -1 T_ / ^r ) Ler , (r (0" ' I' - Loo--'f t = (A''') ', n'' _Q.a,-,1-1. o-' = (!--")'t . rt'.n ' =Q"')-''l!r' - @'t 1)-',1!"; =@rt1-L,p-2t =p-t;a'1.n-rz -(n-11'7*z | _) .-L =U-) . @')-'=1n'2. lPro"eq
  • 17. -lazorem ., Eveoy 2,;.1a"re -n;L'rir- can be, /'< ^-/"-'-'- € it-aquzy e lpoeAAzd- a. a- +um oh a- ) tn -n') ' whzne,4/a syrmol:r) c a'nd gke, *yn a)";c -roo,Lt'jx-. pnoo,Ei l,-,e,L,A be o L4en" A 1;(/t'n')- LLa, l'qu poR ah- A . '>ar1Lr e o, ott") ,. . SupporA " B-- !(,0+n,) c =+ (A,A,) "'n-B+c""..@ ..,u,,l+ U.Fn,)f --tr1r'*o'; =iLr'-u't'l -- | ta'*r+1 -D t-t t I ',t
  • 18. Y nw, c t1) A)) ,----"---".-" L!.-+ ,[^ ,, C - zkew t;lwt e,tfi 6. -n')7 (A')'] 7Y - ?-t L.^ ' 1, r' th.f "/4 Fron e !b A }* t'l'-e 'tu' ny'r,1.[t;, m,^tt))a' ,Ur".tuzray+ *.+t I -,---?---,/' 6 t),*-a)-1"*: /qJ ^"iO, a)' .$y m),uli c ar,d, -ak<- xy,"n2t'r) a ,Aew ' 4Y'mm4-Irte . Srch tJ, g - i.h!, "),q_t p t tl orr) 2P - A-f +) p-+(na*/) i^;loly , 9. I (A-A/) "1-t(h ^h'w', /,J *vre anly o>,,L,woy o/- </pte4u.t, h A tLe Aurn o,t' ^ynhttte o'rd -x,(<* +yr^nzJai,. r*trt - A.^,+ut',n" Pt ^ "Qt i a. e+q)' = P't Q' n)=p- e
  • 19. M,i) l 'l I 2 .L -t -1 o b;"d n-' Lr."tJ ] .i,, ti G;u., T,n .L -f :l ;) deh(n1= 1 Z a tlo L '! a o -al + J (a-6) +t (6+1) .-d"*(A)-- Co-bocLor.ts A,4c :l -"'l * l.' lr::l I ;l *I-l -ij ""1 '.1 -r a ll I / - l, ol " lt,-4
  • 20. o o (6n )) 6 1a-tI -@+1)' Q,r)-(o q (a* ] L 'l .] 7 oo 1. =l --LA')' 'li I =[; ..na.ta) Io -L -] ] 4dj(4) J<*Ln) ?,,,"flr ) o ") 'I
  • 21. b;"t",ln=11 o Li: ThJ', 'li i L1 a A G li: -li t izl qL 20a;- >oL ' , jhz () o L ,!(t-o)to@+o' L "l?'"t .L il .,laL(n)- '- W(A)-' *tr :ri li ol .' Co-had.oP ae A) No-, -:; oo dl + ao Itr "il "11:/ 'l o L at; ;l1 aF -1 1 o 1 -l -ttlALj(rt) - (0" )'
  • 22. Now 4.1;(4) WU) A-1 lt o ol l-L r o I L-L o ll i,lf t o o I :r f t l-t t o i / t l-: o-r I lrLr rlz o o) =Zc> z ol la Q 2l L- [r- o ol lotol I o o 7) ^- nL^ lL o ol : I,r t ol L-r o t)
  • 23. OZ o2 o a -z '[i liL_ 9/' 1tn co,!cu,la1=- Ya-? B' B G)""n w(s;, L .*'I,h l7l2 ,l;l c) a 7 2 () :l -tz:1.1,. :l -li:l-li:l l il -1",:l"li:l "l? D zC>-") B;B'- 1 o 'to + ':: 3 No- -, co-,b-o"to, o)- -1"- 4
  • 24. r q--a) '-.1("'o) '+fo+ 4 J .l @-+) -(o-+) LO'D) -+ + o -+ + ""J q. + t; vl=+l ,++ +- o , . nLj(B) - (p';' = Ngw, B -1 ALi ( B) t d?J ( 9) -+ + + -+ (a-'rJ o o -J
  • 25. )/t J/L z . J/L LL .t 1/z .-.8-) B = I [" "'f l.l , " " I ] lt z a-) |" L +o*u - f ont* o- Jo-',*t L._;-" -z l, or o+L a+o1D "t",1 ts9
  • 26. .E Fi,d t)."e v^luu, 4hd2a- v 7 ,L t -)) G"; k' / *-z -r z), -n,* e.z./ $;ve thott l-r-, -"-.) V-r e+z/ i) 5o,l!', @ @ q. gd,,@ -7 -z /r.tdr 40 -7- -2* -* -.57 LT -7 Hene,wz ye*.., .1/ -? = a't}" C X-7) 7-t = Lng aLt=2 - l 1 ,-- €+? . 7,y = 3- 1. /T .? @f
  • 27. *" t"j, y 7 --i 2r-G3)= i=1 et.@)aan J 3-1 -( )tt !4 1. tl ^L 2L+3 =2 .t- L guJ ry x=-L ar.rd Z - -3 )n e{ C + (-3) -_-L -y _=23 =,a_! eY=-3-1 A-n,,',z -,_ L, y= ,4- ,Z z 4 & *= @Jb o.[". ,] o,d_s fo LJ 1] L' Aho,.t )',"+ /n, o,t,, , 4) (p B) _J ", -,t, ' -f -'>r' / t,nLv?tr .f4":rt -/_ o l: ,l B l" 1l Lr 1l lt .l Now,r' 8-1" tl-lo sr t t't -l L' rl l'ol-J - ta I l I -l L2 )l
  • 28. :l :l ,, (a+B) (A B) L:A-e. f o Ll 'LZ ,',@-te)(n ",1 1 ",1 .',-[Z:]L: - fo* o o+ L.-, o+ -Lz =Lt ta 1l la ol f^.- - lY 't' LJO] - | o +1- | ^. -lo.)l I a 1l Io l lla l1 )ll1 Now, ^L h =A A = :l ::;l :l ond_, B-=.B,B o* o ) , * oJ
  • 29. o--t-' l:L- :l'J-f.2 I lo "l = f: ''(A-B) [A-B)1P'B'/) "L l: t: I " zet-11.9 Z L J o") . Srnvulot olt I I L =1(t-*)l + z -+ 3- -C,,I'i 2 +-/ -+ 3-t z 2 +n ) l-9 +a- LPtt"'et 'o-lnz "5 I , lt- -J-: o -ta*L/ ap / 2 L =o
  • 30. - G-t) Ltr-3,()++t 2 3tt- 9*-zi-t3zL= =)-ti + Lz.a - g tt --o .=> -/L L/,--6t+1)--d 7Q-,t) l-* +x -+r' * tLr+4) - 2 a )L ('xz 2 t 3+jL). o ( t-s)---o )L= O Af (: zt)+7G o (-Y =" + )L-3=o [=un A^ /Sa yaXtire:). v o-[tu, oh- tuAr3*no*.;L inylar'
  • 31. i.,r-zcir- equ oj;on ,A-A^^ : S,l'ove *l'?, ka"Llowiny zy+Lem ob hr,eqv ecyro.liair,rb .",,'L L^< Mp o)- .^oLr;x: zx - 3y -r'9-z-L ?x t+Y -tz --to r .17.2?.J lZoogl t* Gi,en hh"J., 21 3y ++z --L 3/ ++y -52 -Lo tf - VY -rLz -- 3 e.tnoJjonf ,n;tv'z-u'-nJ x J'a?r a'Pe 6eLow ', 'Te given "/rrtte)1 04 Con4iden to,l Ax--$ .',X *A LB -3 +11, 1 frl : :llll l':l "* ft l- l1 +.L -12 -3 +l - | z + -t I l' I l9 -7 zl = 2 l8 -3t) + 3 (6'+ 25) + + (-a-zb) - ZCLT) rQ { 3t) + +(-n) -- -5* +9j -16q = -LLt tA)
  • 32. / W (A)---tzs Co -b+1'to'n 6P And, A Ac= |i -5 |" lv -l "'!'l 2 t nl+ -5 | 1.7 LI - I-3+l l-7 zl - L-l e+r " (e+-?r) L+- zo2 - (-ro-u-) ,;] -lz f f ? ?q ) /1r ./ -L7 -3I ^- -t "t, (e+e) ,"At4G)--@)'-- -"1 :+l ,11-),4. | -,, -n- L r+1 J ,1/ l,t _11 -] 22 r']
  • 33. 4A (4)nL - A.'B det t rl; illi, i) ;l '^.. l".ltv I LzJ I r I - [ z't [] I Ljl Nou,r, 'l ['l ,"llvl 1?) L3) ?,1.L ,.1 , f -rz -22 =.,,t1- J, tL -'-l I _4r -1 L' t i-tz * zzo- -;-*-3r-LL6+ '"' l-+t rc+s r f ,sr,1 - Tztl-ttr 1 lo J *.L; An) J. Lt7 o
  • 34. I lr+z) I t^ .., Ueo,o ff4SLore Lhe l>r-urcwtn& 'J,* *ya d? ")' lJrir "/-+Y+2 =4 a y+z--z b{+y_Z =L 5oI"i Gi,en thol ,A:e X+y tZ --G l-V *? _ - 2t'+t-t-^ -Tfr4 $ven e{ )n *nz mntr)x -rjlterl 69 5-taw I l" t tf rt r r,-t l,-,,ll!l=l;l lz t 'tl LzL y4 C"rrulq' hh"L, Ax: p .',x= A'B Now, s4rraL l', :'1l t"l lL 1-rl '-l(r-r)-t(t--'r' -- a+3+3 --I -'.ld(n) = 6 /
  • 35. -7 1 l l -/1:1 i +11 IL-LI I z +lx rl -ll l'-rl It , Yo;Loe o/. t., nc- ::l iilf -liil ii/'f t: o Z L 33 3l l '.t j3 -1 a a'L =17. nq(n)1)' Ae.j( A) -a z L I-t - - | l, r., o I ll l3 J -Ll d"t ( A) 7L -3 a t -L =iL:
  • 36. N, X a1 v) f *1 lv l-la I L') til ,,1 l 2 z o Z .Z 2 3 1 6 .L l B lo 16 6 tz tt - 1 o J', .L1 T I L'1- 7 3 a e T r_[ cl L ff 7 L3 v'-2 4z--3.^ ,p- /,.ib^ +l-e ]t1rcf)e ,4y '' I2- ho-Mb;u'). e trLo'ub Jl+ eY -r t = 2,t-3Y + Z = -7 ++Y+eZ -- GL'ten hh*t' 3t+5>-+z-- 6 2{_3y+Z=t -L ++2 +ez -'L3 'tl"z $veu ey*l;au )v tw 'mJit' Ffo'n ate ,s.p'alten 6;,' Le)aw I t L3 *hz, eo et*ic''"xI El sXove pJrir 9o,1"",
  • 37. -+ e ],ilItr|=L'l 5 -) llL-' .- Y A'Q t 3 + Coilza Lhol' At-B '[eLLn) ' l1L-' !l-, 3(-tz - +) - 5 (12* r) - +G'3) <t-24 ) -tt-.. 1'2_ - --/ < "j -66 - 6t,za *l: P, 2l ':l :l3 L :,'a - (:rl,i i) ue-+) -l:, -.L trs) .l" , ,tr,t (4) -- A"-l+ Ag*", Co-bocla, ob -j 5 1 -;l :l1: /-re-+) -ho +je) (9 - lL) - Lj+t)
  • 38. " . / .',frELA)4!'). kl I ,il=l+ il L7 :13 5t t.l-tL) -43 au - 11 _ L'L -7 -13 3+ -11 - +L '5 -J1 "19 t ,- p-t - 444( a) a+ -1L Now x- ['B dekLn) L'L -qLr dL -1 _+L at -z-lfe' " llr J-LeI L13)
  • 39. t=3 : ! = l 4ru u4*, o,p- <E4dJttth4 o)1 1 l-i"32-z3D-e1,1- 6tl-+s++o-t+3 l I to-zs-z+z 1 t- t l- +szl tuI-ta l L-3aLJ f.l f z1 '1rl-l'/ L*J LZ) lhc.k, Jr<+!y-/7 -,13 +x +y ,122 -- 6 2/ +9y 3Z = zo eqqoho,, )n k ,a oI ',L ,t"r,n -^lr t 11.t1 fr1 ) l+, -'"ll/l=)"1 L, e -]lLzl L*J E 9,tru" tz b oilo-;"y rnuti t mt*hod i 3 /-.+t/ +x-+y L'( +9y -7L -32 >r,^ r n.verl 1e, ?jtven a oe ow ean be g1"q,
  • 40. I Cor,,jJtr/:'4 |X--A -''X =A'B (n)= *) d2., lVa l3 5 -11 I + L -11 | Lz e -31 + -f,i + L 3 2: ', jt'l il tt'l --3 - t L- r" rZ+)-7 lrL -LJ -- Qttoe)-Qatt) -@xz+') - (o - 23t - 1e3 (-s* tos) *lItI -7 -ltL -3 -7 -3 ^O- ,-'Co-foJot 'k lL 3t-l? -7 | + li .4-7 -JL -4 t) 5 3 2+ I toa =l-*s luu
  • 41. i,l'[';: -+3 t Nl. _, X 709 _ J't- 7+ = 5J 3- 17 | --. I ; | - l1 tr I Lzl It .-,Ati@=@r'- -r AU(E t& G) 1f Lot ' ,:.- | - a- I z+L -_n"B t f t-ttv:z.38-ra 6 )7 l- IeL +30+ !6u I .!+2,-roL - 3c-d L rltrl -"Lo ) f 1 I-,_tr1?_l LAJ -+, t -,1? - 13 3 -J] aj ( LO ..'.r--Irt=z 4V.u^ z2
  • 42. o- )y1irfl4/+n( v,) h4.e ' A - 9,f : Giu"" vie @ fuPretztJ'e'v"J:t)x 4 "a l)'a 2il c',rd a l:2):q"*t ^'Lt, ii2'.1"[i: :] t' ts c -3.1 I r L -6 i L,-, -*J =V2-':]V,i,;] -L?T 3Jl"l cz L .o) zke 1l f + L -Y I--1a i. o I l:3 -L '7 | -) ,',A, LLeh) A+A,. d{., A-A, /
  • 43. 4 4') *[i ;,1 ,'il, Llt' !, ( t+e') -t f't tls z -s1o Tlz t -e l -, -b L l+ 31t -+1 lz/z t -1 | l*+ -3 -]l a) Ah-A Ayhrwt' e 4 q o.b- tnutrr>t. f + 2 -3.f l:L l -"1 L-t o -*J ,1 -a4 el f e@l qn l" hkewytnw/ ftc _
  • 44. I tgehva^u44 I E;aan ",o"7o_,-.--.,-_'.._,, --r-.,:__^;zFll- n ,,,u UeD-Lnz < ch q*otler;4Jic+ Cho:,acIe, ^,yL r+ polynom)J oL t -4qt<qtq t"*'' : 7*.G-E""t^""t l4 wi4 $:ve o polyno^ioJ", *ru"n )Il ," hnn ".p",an c^qYqaLeqj*iu polv>on;^J oa o- For ettmplz: lc_. It'-/ ' Ilr 3-^l _ Cz_DG_z)_ z -- e -27- 37 -1,>"-2 -- *-ev- + ch q'paatefi^liu elua*)ot lr cL -.L?Qqle bq*tt : w e cal-?, w 8LQqre ha.LP;t A. 'fl,e. eauahon I A- )Il =o ,i), cuLI-zd, l12 cha:r,oaLe*h4 eLuo*;on o/, tha mfrix p . As,, ;i- 52-+=o
  • 45. e,yen v a.Luz-.gr"o,blzm' A be a -gcLtrar e .r.aoirirc ' "i,/-h etz*,en!* ato'Tt''*'* )L ,. ntolrt a YrLtmb€)"7 o'vrL t) o, ' tt-" ^w h )-hJ. At - VLL . @ W D"Y;,^z' gJus", r 6r[er' " nu a-V;t7 9.b thlx zaxo vaa f trzh; V- E 49'r, vauz a-r' ]6Jer* rool' on cbdqaj'r 'z)' u' v "lY< ' u -: Eigzn vedfu>'o ot' chaYqakv'J|. v<c*on o'E tv,zn r'."4' I ror^ eqh g., "u e gd.' [q,r , o,, %,) u - o t-1 l l',, %z-.7 a-2" q,, l L- , "", t o,' o ".,,-,/ 9t r< pre,rarita 4z* ob hamo1zt'eou-t"4"*;;'|". lA- zI) -- O A a' po,(yrv,ar"iodQaLlo}ja." ob- dgt'< ' n''
  • 46. )LTf", Z: t a-afit Now, chqt'q6fs45/.;6a, p oXyr'avno n--lzz , li::l L lr- A)+a'- 1).a f L4 -) - ^^,'-z_rL4 2 z u. 1 /-tn , A'^a= l7 ll l" =l'ilt )t ch.'rq oter z i] -)[e ool ^ . I l^ ^ I r 't t" - - l q zl Loaal :.1 l=o l l I I 2-2 L 2 3-) 2 > (2-v)IO-v)(2->)-2t - 2L2-2- ) -+1(z_3+z):o ) (z >) (e-=t - zv+2.-t_, -/ r -- b /t - .t'h + ZZ- - e Z-+ j* - ++L2+7-7-,a -.'-.i' 1!i'' -tt-'t +t-+ 9 - h'' 4 - t)'t tti-e.o pt t> tor,Jtprt&c -t"-
  • 47. E r=j*4 " ,J "- f chqo cfzr'aLa ^roo* ! We l(vraw IA-7Tl= o 4*-72- rttt'-Y = o => ^" .'>"- 6'),.+t) + g2 . o =>z'0-a),n [], ))+ e(x_)) )4 ,) L2. L>,r)r o ) O-1) Iztz-s)-t (z-s)l -,o .. (z j)q2.11(2_9)_ a ,'V-- .t t_,, ,2 .'. Ch a'raa*erLhi.. ..ao* ar E;gzn y6Lu-ez oY 4,1,5 , I ts
  • 48. s.{: th"+., ,=F /,h-< elsznvaXua *zhvec+,'rJt o,, tl l o IA- t.+ ?1 qnl, *h< *h-z '".If x :l ch ar acte,v,i-iu e g)-t^l:,ian ol- vTl-a -2 rl ) 'ro : ,,1
  • 49. @ 4.@' *elt' U.* , 1", /'z' be kL-e eotl P6nar'l 7'E e'r'yznuer*ot, .lqJt , 3=[+ ca-ne^pot'U4y La l-a etX<nuJa t^ L/-t-)rl-_a =>lr-^ n ll/,j,=o | 9 t->l!,,, 1 L ) L- -) rot, A-_ - b, f t,- f--E) 4 )r .'- l- . " .ll '" 1'=L t L-cr)JL,,J *- [a +lfz-t 1'l9 .ll , l-_o I l xz I ,fl"r.e-/r1=1"-l'' L9rt.6,rrJ L"J .- 6aL+Hv-"-o "',.@,' 2lr 4b(L=o - , ).(D -IILT e A yr6 .A olu*jo r. o /- e. g 9otf-or 7r=o ), ey @ , ft ^- : o ' .--- I
  • 50. e1"Aq@ dW.j 15on ) =) fle"ez, e)yen F, r 'A - ]) "/, ) t^4 -.-@ ,ll t. q.l/.,. a (/2, E>-9 '/3 2 v<cJ"t. .'>, / ^ u) , L >"Jat"" oJ- @ *;,1! be' ,) ?). )., IW ch a-aatt<,rL';l1I -1,' Lr--z) + I f- -t t",-tl F- l-: * | l,' ) - o L7 .O] L'J F l-LtL ++r= I - t:, L 9rt- e ". l 'x.-9-( -o , (?) tL -6/t 'o " '@ -) -) ,., 6 9 llzr a *t '9 o,a1" -( n, -2 @ 6L1't te<
  • 51. tr:J tt) YyAI L I (t- >)|cv"a;O )) - J1- tgt,z _s)+s(L-1,+3s) =) t t-t)(9 -,)- 7, ), r) r 7/1, - ' t t) )1l+ L),') /..),2-,)^)-;:=:'J1 t b ) ?- { ) +)'- +2 -rt).- vi +j6) - Tb = o :, - )7 -t V)-- 3d --a - )t, l. -+?- - o rthd v e.cLctY ^ So/"I Le) , A= l; lz Now, c hqaaCle .Lh-Z L.tzn oA th4 v ol uz4 l"L- qnd 1 5 l_ rJ t4 11 'l I) 3 l- IJ -)) L irl plunan:-L (x-)) 1 3 Cn{'r ddtey;riti L c-:q ), 11-zt) =o -/ Q--?) 3- x E-z) JJ A"V I t- r) ), /
  • 52. 72zt, 2 z' -92' - ) 8', tgt, 3. )f 1V,t,-9Ztt- ,iB(t- zt. o t Q*z) (h''.t7+ ts) = a (h'- 6) -3)rn)_ o lh0 q-3o-(,)l=a- (^+z) t[? L)I Copre1p i1 - to )al ",Llu< ) o&u ox 'lQ-z) (h-2 ,o-rr- o ' Lr 5< ,) = - v6lu4 IeL.<,t" t,y t tLt ' ahP"r"zt o,h- q'4 t--^ytlr t<( Lo, I xh-r I 1 (t v) 1 3 3. 11-)) ll,) llY l=o llz I :l rh4 cnkny ln-L ,t-z) ? -l'i ': .'"2? | lot tt1--'Lt >)v*z I lal L'l +r+ttvl 7l L"l
  • 53. 2-'2reg' @ -^1'l f u-+y,y37l=['o1 1,*z"rzI l?I Lt,L+y+tzl l,:J '' 3t+Yt3Z - o L r ?.y*z = o 3t+y+32 ja I g, *)1 b<, +321=la1 +z I lalI t-l -zzI L'J t-I lz klvr, 9;""2 , b;r# ond .tlrind egh wz ca, ehoatz hr"'k and, qre zamz 2 !h-erubo'r", .S<conI - ntt Henaz 'v"Jhb. -:, . - --:- - 1L+v -22 -^ - r>+t =6 : --, :- ,- J L1,1 - o - -Vi e)Wn .,re.ioy "r (_1, o, Z) 2/+ y )L+y
  • 54. j:herc*otz, hca r ,bir^tr .t< "t zzjtj 3z 1- LJ ..'r+/ + J L ' t '+Z2+t 3t +y -ZV Lh-LrQ e.y' at"e sl16ay,< )rirat )qJ1IZ ohl ae.dhleA .O z :a Sint(," Lt* /l'tr dnr e , on{ 3tl c-ah w€ c ayt ChaaM , t){ =A -x+zy+z _a 't .l -- 'l e1y n c''fe ,r,,i.lo.Y , tet ad zn) ,-9". L -t z :1. ,v.T " c:Ju, .-'.1<nr< '.1 7 _2,, _1_ te7 l;!, 6r =f: l LoJ ;u ,lz3, 7 -+2 t -5 w hz'1 _(
  • 55. ,t+ y-r3z --o L-Ylt=O ) t + Z- rX = a 9)uc{ , Lz.* ayll 3n) e{ ore -ai)e;,iqy, hr',erel'oy e, ,re c.1,>) cotual,pt, Jz* Q ZrJ e r> ' '-e/. t'Y +32 -/ - l o ', I Hena-e e-4kn vecf,o" -i. (1,1 Hen tZ , /hree- e.+52" Ve<*oy4 Lr,- L) L) dnd-(.1,,z,J ) Jtu.- rr3 2*- ' -=--- ,'J 9? th-e e'+'.en notlt>t , 4 1) aYe (- Lro, 1) v)< rt Vecror^ft F;nd Dk *hz VaJl)Le^ ct, d = lE o 1l lo -L o l L1 A 'J -1, o a l -t-J lo -, ol l1 a tl $ G;,enthd,4
  • 56. I c t)ot'aOf . r^;L U c,1u o_lr'a1 >L5-v) (-to -t-Zz-t) +2].)+ 2+ ) = a a L5-)) (z'-sz-zo) + 21v= o > 5)" - 1t, - 50 -x3 +3v. + ta)+z+r=b ) -)3+97'- +) - E3 = o ) -r3 -gi} +,1) + 4t = a t 2aj Zh" -1bh'- 762 12+a + -; *(z*z)- toz (z+z) t2+0 -SQvz)Lt- - 1oV+z+) --o f>+z) ()'- 6)-+, +2+) = o . ,) ( "'z) 1ltt )- 6/ .+ /1-b) -D L +z) L-+).L^-t)-o 2---2,+,6. t lntrL=; t') a o - 2-2 10 a a 5-) )(.))t( 2"-1/(eo)1-o Lt -."./.a , . E,yn" volu< /../- 't e1*o y4 t, be *c "j i! Lr e)- .Lhz , oa pornnt ti:l &Jz. aL dh
  • 57. I I s 1l =,V xt @ be tuhe^ 2.21= o Xz = o r:.1'L^'l e44' c) 1l :l(et) I .El v ^,Iu-! ndiay f,o fr,h<, fn-ar12 = Itv-z> o I" cz-^) I l,t o LE'))/, rt3 1 LL-7)/. I-1 tt r(v,z) t, I ,J -6rte.4po w h_!h tv- 2 eL"@ f7+L, a L xt*/r, I-J Trrrxr=a, .') + l(?=a tar ravo €qb /) ,ri-!44 a a].
  • 58. 7 flenee., eorrlpond"vy et52n v<ciot -a -/ -l O I /,) -l |L",J il ll l- Anao V-*,er/'@ ^.t tt(' frrr,"I =f " t I ^1,, I l" IL /7-t/3 I La- .,)tL+73 = o ,Llt _, o V t +tr, - z 5,n(2, Ll.,t + 3.pL et- l^JU Cqb eorv,.tJet la* 4 /Lia|. a -61, =o 7L --o T^1", y 1.,. h ):1.<n /, _ so, teaar2s v ec-ton b, , W lre, , eqh t- | 4anz,Ihrzre&oy" € ,Lb, 'k f.= Ltl @ wia b< -1"1 L'lr:"1
  • 59. hn , u,t taLil,tt, lne-u^ ! "t o"l, = .1_ 23. J 3r) --n )4 +,2-"s P1 - ^3 _b/t nz -o a o )) et" -1.fin y 7, -, k , 5o tl'p, 1'aqQref, )" tb )1-) ve (taq .? /La , 42 =141 ?ov ft'L -non-*Lze I 'v4.*a'' x eitL, -l'l rz) -=. J v " Jon, .t)" r-Llz) n orm*I)>e) a> a i /:t/ barmdt ' tt, 7r" -+ *') + t, fu" )=-2. '"')<' 4t, = g.ot ,:Lgan t<J"-naave- LEl "ndP'r^ol;zee o'+ A a v " rtor, OL'. ) ) ta kaY /
  • 60. Fay, are. g-ot e)gzn t eJo, ,)-u x''1 hoeryq!;r-4 ery<nvel",Lc4,) con-etpen&nL foJ o" l-"1 11,I l-) | la I lo l we,h .L:J )ot 6on , "-rLud ,.Ju., kt+ Dt L I (.-t;)'= Z ) ,k kt=z .l ,'z d v<cJur, eig<u v<c/o, co-r,rezpandiny -not1act!i2s K + o-+ L-t,)-=1 ) zka:1 ) t<',, r 'L ""^r1- .crr apooh4y n qrmali z4d- I :? I or t- L l | "_ I )t "r, I lel ) p I L ,L I t n, t Hen.<, Her,c,e,,
  • 61. etSun.-L ho,ve lDt =r:1Lxl For, V= 6, v.'e 8, ve/-^ut' ''r < So, bor not"mJ;2aS vec,to'r, R'no-+k'=1 -t k. = ]t, Henez. conr'.t,p:r:"y _r,oo r.altz-zd lj" I ^' I il lo I lol L-il L+J fier,tz-, *tz * r''na eitzn /e(tar (o"t,o1 or (o.-)''/ ' (f o, (-;,'-i),(I o, il .i (- i' "", l, /" :2- o't> or< l d2 / D -/)
  • 62. -hqunt ( ,^ .f rt- /'^ .tl tl ',v9 -ay na mLtIoh laot" rn i Evet y ( o Jt , 3LtL,>^r<4 .4 "n..^,r- < h ar al<t;aliq e{ [a,zt 1 o Uh Vefl-b f <ay,!e.y Hq-;JJ"n *hzorcm l-o'r t'tz v.,J,)n , A =| t +1 ontr /)v L ).14)nve,,e. nho. lz 3l etlfe ^ A5-+4n-763+11k'-A, joT A d l), lr ^taY ? a)ynoni J )n D . SoL"I G;,r.n kh,*, f 1 't=lL +l lz 3l Wc k na-, ^l , cnaPottrzrutkc4 €g" oL ^6-I.,t p ^, I A' zl l =o " lt a + t I t--o lt 3-) I l- t > (1-v)(s >)-3 = o ) 3-V-:t+h1- B-- o .,a--+7-r=1t
  • 63. *7 -T=6 Aho^,, l(r])-o be,l(4)=nz-+n- aA - CcLn ,-,+(v)-- ,4e ho'tz' c.; t(r]) Naw, n' L,H,5, I [,t + ] ] + l:nn -)1 3l lz z l L"-r,-l -r*: ++)11 'l''t s"'I t,- =le '11 L8 lvl ,_A', +n-5r -lt xLl- +l' "l -tl'o ls tt1 ),2 t) v Fq '-l @q "l-f'l" iil-'ls ),1 rn 9-+-t 16-''6'"1 lr-,-o tt 41 t) L lo "1 LO "J a,H5'
  • 64. o o -J ) vn- l. . r. , wv. dJh h (2, _ (z--+t-v2 yt-+ze-vyin 'lt-+tu- 5vz- .L: +l -r I - n,rL f)' - 7 2t -t Lt'- 2-taI) tJ2",2-JoL zvj -r 8)"+ ) o)+721-J 2) -) t z +(n+tr) ::l ':l1 3 ,t 2 t I 1 5 il1 low L _-- 9)yez,6n2 zoJrtrtq ))' t b c-,"a,t<-74k4 qxn I u.,it-,. q AL >A 4-A 4 +I 5n "- - A- +T L / a_+f )
  • 65. ' '' L^,rpo, go,lyno"-*,| 0.)r LIfta- a +wL) )n r) n e A1 ;L hall (n9- +n+-7ne+ ( ++tr)^ g- Gh, 'L "t ,+ub-mJix- oA- ?4to" fh4 1.ta*Ltn qra .fto have Yqnk 'in )nua'" v7(v',n- 5) 'J(n'- -L1, (v'- +1 r)+ +n-9) lx-(d r.) -f L.fl Kqrl A nan. 2216 7nJ' x 6rl4t an? ; W.F<ten* ,b-tom NQ 9F A U. ar' qr"bi&a',"y mxh molt')x 6veY o. k'd L F ' "fhz- ^r'qnk o/' *hz- "'t "t) t 4 p ,/+.t /"*y* v "'luz o.f r -bo1 w Dev, tun," entl t n,n 'Uj.b'mat' * ob- fl *)tt" non- yonia}","rX.fu*evnun">* " .l ILu"t o r'2' oJ'T O8 In2 ^fa,nK ',tL'r'tbet o f (o/ uY'l M t Y) ok*vJri-Ah h",er), in f,<,pen{u'I ftu'e-"nJr; t y, o)r .modt)t ,
  • 66. o.ndA*@ j"'e,Le^lz ,Lnz , ou-z ua ) /90 1:ha-t th,z efln, 2* +3y +Sz = 2 V,, t3t.2t -B t* u6to-7=-o hova,t) Np so)ul;o, i ) a una"z -+o,lul-ion 6t) frn i #;h;Jz rl kn be). 0,6 z"/ul; ., , So,la.' We hoveA7a-r+ lz = b l f 'l =f ?-l lt '''llY I l') lz 3 )lLZ) L')L'" rnz *y;,tzq ho5 a-rya zo)uJ.'on j'b ,an d a 'v i,b. kL cct- e|b) ''te'rt '"oh)t jt oy l qnk e I' NlJ> veqrile4 Lhc*' ? ? 5-) = Lt(5,v)+oit 3 'zl ,L 3 ) l tt"t kn LLiqa s.],,kon ) {! ot:d- A h"v. Yave qny ",iue. Jb A t ll'z z y;y'e'm'tu hoverr o s.ftli" ko, /v. o'r<'vott'z't o/' U 'L" r w l."eI t!.2 t |'tv(4. 2
  • 67. .r''.':'-. * ""t= *L ,l oo'nz- Y* Y. Bq.t A ; "'u L Ant B, p nat' a/s tank 2, w),.7t"a 'Thut,iE A=5 anL )t -tI , frLe z>,/'^ ov< yro 1.,o)r.L;ot ^" L ,* A=5 crnl ko ,:rtn- -/U houn a', )vb)n;]-c o), t"Jq,lr'ow. ft=lI L qe 1o -f orI LL-,7. *;Ll h Ut?, I Ltmxr
  • 68. Boulr L IYEqI( ll M0 ^, n {l}qe}Kq- v rd fl q4l oahra'/ I q A fl v^RErr+l^.-- Qra+nix() 1n^f{'^^+J *"+t"A^- | La.{'ce€ --n<n'{. S of n-lr.i "s csE- 2l r ri a3 12-. RI K -n*".V* l 4,".)i,4<it. J. ,1 ppcl r^r"ki 19 I + ?nii- {rrr a[6(1 ' {. E' Exa'^e Eohd" [Aa,.r - - - 4d ooh,r, 'o-' Ta+nix-g I ?r 4fl.4- oat"'nr {lrr.(1 tio,? '6 I l' l l:"1I E) I S+*Fe -^^+",i1 -'t'f ""^+t;n- ct gooq *!"-i.:f, <rao4 r,:L<n t!.< "* t"lfl' F'-.e,?| I ' ?l':,,;JllJil;"K'^ I 1 e -'I lto 2 2)axz 'r Dr"go,o 1a'+; :liopo"-,!. a<<1 e-%r'r'n{ u5]-,?..nO lLt'- o ' :-l,,' o I,J am"(a v r'lc lo
  • 69. 4 s""J"n "o1r.,6 g }l^go"- 1rd.({ : ) , o e a' I ,tl (u^il r"vftriv.) ele'--d -qo1c Q | + o 01 tl la i. al l6 o 1l ,= l,:' +' oa'.:,g*e an"i.ft;^ "1 t ='T f-j z -zil u=f:'_i,:l 'e fr<h " 0 0 6Je".+i3 : )iagcn*t <11<3- 9 vr 1tF- I t Et-^ 3 J - :t tr 3 t -2J
  • 70. A- ft.o.m?.s4 9' NulI halfti)L t Jo, S$h"Y€+nic )"!r$n A*a",,t -.;-: i.".T,r it; -1 b- 9 -3 1 Syrlo'€tKie ?r!r+n) ^T ( a e ':l A=l'::, ;lI e 3l lo 9-t , -Lt -_t-9 u + j--tl . ol la-r{ I.,. I l- I Jl' SKccJ
  • 71. r -l: Herr'i lid' *'Jn ^ '" 1r1 r'^<.ltit{' irede -6|(r 3C,T4 21 -tele 4(or ' ?r?r_ btr(6 1to c-'rPlet ca'.- '.,q-(.ji- ,.+nr'' c$ ler rl1r-ir' SK (r 'dni u< +@'b|a'- a<('"r - A t-4{ 3{4Td sgo 2rl-elrrie r^'S(i^ ?<fT tg.A* *.*niN r-: o -i -<.q| ' .l . 0 "1 I .1 ?r ' aJ oflt(oal€- of("r utKdl$- k-r <kcci ttrrlrrlnu'' 1 il,J r ) r' -il t; ]l x. *l'A L-'! tl' nv,.'r{io Fhi Ia= | L r! -(6 Ca/hde( bf q5{r{ aT e o 'A h, 't i I .-l*i' I s 1 l <.(r 13' 1
  • 72. l - ^J- ba.tnlK-; <Ll 'qG# Ar' A=B r. c. 1 t I t" I Bt ,-.,i- * :Co.Ir* ?F ,.-'1 , . " -- , h/).npi.Y I 3 -- - - {'l r 1l 'ai-eara,f1 tdr-rix ? fr*- ti l,- o r -{ Ar| L^ .J"(t *a{' 1-atnl KB r .'o. ERIOd]q a- *= 3 -C ritnt eedaAie. r4, NJa{{v.+ 1'l 5-lc
  • 73. I F,{cl*S t:?,3 - i A2 ^= [] A3 L:z I D , ) { { I ( i 1 ? -L A--e.A o3- a'' e $|"r-pol"d "-ls,i,t', 8 K= t,:, 'l ' " <-a a1 l..t n: l-r -:l L Fy= 1 ,il^.(< ,l is '?""[e i"'a+i!'rv- Ao--A R T s a- ')' |J r^"'{nit( -rL" tr. e i&r',tok-t 'Y--{11a.' -0 r+<,,s,}qrry..d,.iy.: ]i.nlrff itJi' $Jrle7 w anr ' ' !.<ln''y. qm' s 1=o s1 9 l0_ t,
  • 74. Non-si.6rrr!*n r:, Co-5^ul"n n *ni"-: 5{"*[, w= le* t (3-jqei€ n tI r."lrnrv- F'@' ! r"+flir1 G{ AekQ'',4q qq qe(6 ^d-sitde.f r'c'1[l^ Qn;a I -1'.r :?,{{- , a. .{t <<fr;, ff] *o . e al 1 2 ol , a',2 o'3] ., ! -,ilo.aq "*1. I I -"'.t ^J,2- a"lj '^xn .. ,;af an =An. -7 co t1 'a1'r = Atz I ^'rt^ /i' l"' $,.cfinAb' T I 'z ai CoiJE('b( tr
  • 75. - i""F".!"t-l a I ) t l J L'' J i 2 --J)1 =-, -t{ -r-f r ,q::-")_'-l ^ -l- 2--" t --/ , - l-r)"n,'3 = 3 o, eJej'€'^t *.ni* u! c"-J'.cJ'rc | L e* heioK 4 a. "o.lrLl*t A t. *&-j"i* i^"*ni"- t nAt.in r",.{nirl' 'd f t- 1=l L -e1 'l t-"'_ Srr lll?- a: aJ n= 63j .atnix- 'f rnJ 4' lr , $-r$i"r.s< $^',er.sd r".nir- 9 "-.r"t at g}1(r4) = B+0 -1 l I
  • 76. 6<-a6 IL6iue.'il^t D= $ o.eE- 2b ai < t-olr,,],q- trJ.'i'(, o 3 2==' c|e+€fLT^l rj -l 6fr{l L';-d "- rii rc;r !. *Le 3 .r - E{a-rr))-1,rYe-(-'J)-*3(r.' 61'rl-|../-/ ,/ ,-/ 2l:e+]l+34 2 .1 3 1 o :t 3l l, :,J.,.3 r / . 1a-'J t+rlt -rt Arr:i-9 13z I :-(&3>-r) " 2+rl2 3l n:LL-1 ') 13 , I ,, = 1-2 =5 F-:{-9 /. _, - -l-'- r9= a{i: -(.r.r l*.{..it- .sf, ^lrale C0 _-i.^A_l{I + it lo ,:rI A$:t) lr . / = [o+r't ?+l[- e I *1':{-D i3 '. / = _(-:i3lr 3+t._l] l h,tV L_,1rl + Arr=tl),. :+ F.33=(-D
  • 77. o llAlnlv,{ ^L 8-fE(](? =''-J' 'L qJ tzlT h ;jFE 1.3.j . el ?d I . - ,1 r -*lf "-I -rLl | ) l= , -'=lIa] u -5 ",9 --l/ ,rl 1l lY.R ae- dJ oSlp).J lA -",.,1'i "J I 3 l{ Giu.n-tt.e =ry$g- 3K t 5$ - +, --i3 1xt9-rr'2 = 6 ? %-- 3Z = '<o lr^. t or'.rx- {.*. "+ *te Qi'cn q1'*t-: n a :) AX-- R
  • 78. 6 I -1 L-e-{,4= - ti F",o.," 6 -l .=?q,+x :) TK )'x'= l+..'*r. 3 7 I -' 1r^q ""{"..{1 o} + 4tr -- 3 f io& -- lo 42l = -Ll5 +e)=-* &31 = - 60++= 53 'I t- L z)- ( J - -'@" D -IAI - 3i --5 +16|r/ - , +rt--(a.+t).4'-1'1=,A',2'3 7' '.:
  • 79. 39 _tT -tf - ) ) I rne na3lr] a!(6)= - lr 5 * -1* -7 - la, 31 1f l -*lfol "/i,/-") Lr"J ilo,l L 'lit f ; -TI.e trrvot+e al C = I ',u / - '' L'T fi<dnO X-A lp lrE 7+ 31 .o .ej C€) I 1tsr1 -t7 T ]-1 ?=o
  • 80. :!- 2Jq Gi*t .A"t-q+* / U,r- h,bL R-P" ol ^l"/ , + () a o o O T -x^€, Cr.,-"tro. $t-" o4 - *'*..i s ,t- - f z q -!1'r l+r,l =l c ;loL-t l*l It 5 -1 | D i, o 314 r L. ,1 I L 0 'o-;l ",,) * [". R{ LI t r" -1c {--[{ ; f: L* -1 5 ) n'" g a'Bn *"1. J, e,,xt=u . t"/ ^1x'- 9r' t- F2A{-- & K1' O LO -L8 a o A -1 o 1 <t1 I 13ol I r u '_J i k- 3 dG-
  • 81. b =P.-o a - | -5 -1 3 4 o 0f''^' I a LO (a-ll | -/'- -d +' -- /_r_ L l-''- riro urf''Gy'" Tt,4_-_: +l< / l:_: --) -l-l a/. /l&-:x 2. tL t-71 2-31.'vt -3 1 3J o r o ltt ol n-,, 1l1dl -5 1 1l ) 3 / a ro I -lt '' l-r L ! l t-l-u1+l, '+la "J o .. 11,-+ol J--1 1 l- rl 1 - lo y'a*Ki1. o A 1o a -1 a0 o,t aa t'A 1€,Ao{- -[ L- *[ L .,._l'I tte 4 E i
  • 82. ) '-{-L//"J /.7 l! q l:l tl -5 : //d I l-tlll 1 I | ^l4 4 )|"J >) '/ /"(l r qt'I I l l, I | <-/ :l,t:l Y/ s=l sl 'l l-l' l-1 I |) u- > L-o I . *---lntel . { 'l <--],-{ -11 sl 5 ll-1]'.{ 6l o l. ') 1t rl x'!=sc';-n', I i f i .:r: <r''- qr -q I --) R'.,:e'-81 fr ). .L B -f ?/ l-,) *^io .t x- -{. 9 -{ 'f, l /:. L-L (= B -S j <t r^"ail-tl t- 3 J ax -{9 t3? .,- ti} *. ,11 re , v'wJrrtrN_ lonnr .o I t- w,N-4 /it^F-l- rnte "t !^ar^e+ €&qdl -I-t IL r-,1, I n l; lo
  • 83. 14 6>r o6 ,+ jl f r L { -. lo'* + le e r Lo 1 2- ..I'lo Lo. 1 {5 4e 695 oo v" - 55 lKq '"1 , : tl I- sts-le- of !,;.<<tr- qx<Jjot, <J :), v--l- *=-2-
  • 84. **o9o.s A,K -Ll lh< ((arl'Fo!e, 1'rrral al a- frodrrct z+ -i1Jo ^{tv- i, -atA *o 1L= lrcoBacL "{ +L*t' i"-' tw',.t'+-L, o&(j at'. n. B.: nY Fx-or...llas (69r' t 4q'^ ? n'1 al - AFe-sa.n,r (+l F,t t-e i.ew";<+a-of +r^e- di-e4"qr(€- &. -rhen 4P-'= n-tn =I,,rl^enq f i' on! "r'-' t*qHrx- ..airla€A ( goj' # iJ *J. o'&.a c_- + "no-'i-sih*&^r( Qsr - q14- -ir^< uriL a$*yr ".,--e;it,h,trLs q, A it t S ,.o1 On - ve'lOZ .vr..,- sigr,i$a,--. ,'c$, "- "% d!U one he"ap
  • 85. a 't . rt .:l I I F. TT-< 4n.wrpcse- "L "' tnoA*.:t ft-- Jo 1r.. e,,oA,,.t o! +oit orl(qeR-.troof= fl.n-( t_'" bzr - - NA, d=tr'l-- of +..0 -,4',1r.- 1" -lr@-.trrfos<, ln t'u* te .lle h J { .) .J *l - _
  • 87. r !':;o I , =.|5 !J -: t-.J_, 'ili' - it ' l; l 3f q .^f B qre *ro r.{ojce g".eL*.o* ,.--l-no AB=f +heh A'-6 o..d-E=rr A"(q-).---t-tlG)'=, rl q/t.dY I N-')ts - fFl+ lY ' ..- - '/: :l- I - L.' -' ^.-.'f - 4 I -A l . ,/'/ - r 'i--1,, - | r"q.Al . a cr"4r+"(- I Cu...rt nt"O"s- ' h _6 r AlBr^ pct4^
  • 88. r4lR )! - 3 $J n-] A. -Then t"..kix- is, *i{e- nvcrs"- 4 +le ++-1 -41 ;r uinena o,f Jr^e sa.^" oni.rt' "n, s?lo'rre.,!"c;trix- T i5 -tl^a t'v t T} ' I A;i I oq a+ 12- Bl1 - D (r+$ +i5. ^nt{..oH t+ +--L*:l n- - .T _ L4iil lr'1 Ac'tnp.ir-ie-u1'e|(q ,, )=*l is qne -t}'€ e"-'"c{on A$- =, t "rh )
  • 89. 6l -f. , o "l o i=*/ c I o - ol-r I lt l- D) la ao-rl f tr o O - -5lo ) q l; i . lo oa Slwr.V{fd-l ) k)e colrr .Th,,4 f tl-' *l^otn +t-",$ A tA -- 1 =A-+= I ]! * ra.lti 1- 1^q-o,^',n,erasi+ aA a'"lg rt il iS 16q- sir3u$oq ,4 no"'-s$''1''r- q' nw{rtjx- l"a o -g- ae ln€/rre-. q-u[ ? suppose{u$ * i 5 a} +i^€' .lh€ -U?e *xn *^!- aros. *-f ." '4: A * n1,,n . ,' inrerse4:.,ihe ^ *"t;n Oft*rff^ "fu ar(€ batl^ J+ n"& *'& d L - rc, ta h@ ^ -- - 4-t A ""' rtrh F' ,iB = -ln_ c'' E 4ln 4T L [L - SiYea
  • 90. c^rcl 'n q +1.< Re^K ,I 'iL< PFad&Q't a+ tqlo r oR ^-,r{ *. i]^e rro- K.f-o{rr.r }( ls qq 'l^dh f .r, n ei eJTlFrc +q J'-. 'n He-rc m= nr K a.J A ls ro71 si8uroK ' '' r 3i Tr4.'rro fl€ a.ot"&! $!'l'0" s si'ht-xc'RtL ' trar.g.- 46-t= I-. url I rh,rh = r 'n{F / r..,, L_, ;: . . , .: ,. _ i . NoLr.suf,pase .tfd. A = To.iil Is ridl.-s1'8l^|€r '' ' L .-".! si-,ee,A)+0 , 6€ c^,r J"F lti = H3 f t,j--,... -1. L trl^en,- . Ai; c(e *re c" -Sel.rs ^f oii in fi ' -^.rui,. "'J ' $ ' r' f fiil . -the?'lcr. g k {le r"YrRlX L :J - rI ^.. , .1 rl ","]-rdl=[.rfl_s.j,1s,i-AB= la "'K b'1/=/z-c-'KG--i-l1Ar-""1{l^. !r,'l'' - lH.' 'J l"l .r itii-r,;=l.l l '.:'
  • 91. sil-].hr-b sc|, s,h</ 3ls o.-" i^'..*t, af n o"J ele'-4 - ,0 '., n l^aa a- i^ lt{'ah<+ 1^sn.s'gulqt ne,-trl ,' I + te- k".*e }o "n-". si-1r-Un o +F.* s.3 /t t' r.ve'.+q - ?& -Tt!<y ut€- shr" iut,la in'ie"x' e-f 1 w.]flry. n tt^i?€ ' s uf,Pose- r r. -,dl "c. -.'8&.f o'J- A- o. g i. ^iLt o- Y'.t{- o} ar' l-"*€- P'E=I' ^ . *Lrg eyJiarr ar 14 r^tp).1 e".Cl s ldl€ 'c- tJL t.4 g - . {t en c':e 5n d i II I I
  • 92. F- P,- t. , r^i" 1(]" ril7 .'i
  • 93. aJlfftco ulra{- Q9. oS..'tL Ro',,t<d -"lnjl ; f6o,n *liis ce,ae rnn{n'rx- A "-& is en it^< MLe( ffn rq(n A ls ^ - Krooe& "1"oa6e ".{tin C i, rof=o-$- {""d{r'r !( -fe- lo.a G4.f.k 16: ', -tt^"n oalle$- o- 'ro's'!eL'}.fr ?,.A{d.x-' "".!+ +F+o a{I"$. ,^g il sir-plor-c a il -8 r@r:l( G o| Jt'e r'"{tdx + "t r.r^- 2€@ lloos O )e+q!Y^ina -ti.e *o-r' "l r'.trrr( A L -11 .l ,l ;l I ls -ll'-e "o{r.i^ + '51e. rA 1 ,Qs-l r a I : Ll tr cd€ Re
  • 94. 1l ;l Qt+ 4 I-l- I ''L c 3 '{ 6 'j ': -3 I 'r j I_.1 I _" *& I (0'- n,. -2 -a -.f I
  • 95. d 6- oc) oo 1- T I :1 '1 a a 0 a o o 0 ^I k'K o+ w*l{id = B . -Tt< ,1 l --+,' :- -{ -5 o' a, -r '?. o q"<t q {-6, .-&- -{'= d -&s. -C'=rR'- gr '1 ix+et<V€"y4 - -t r-I o ^l -s -1 |)
  • 96. I tr, I + I r _.( l- 1 I z" R -1 ^ =/' -Z -+ -r o- 1i '+ t- - { .1 -.1 o o I l- a o o o 1 o 0 o 0 o -.- r ',2 ) r T-'.K ,9 **{ni"- = f
  • 97. '1x, -h.en {.,'=q,,ar. -:.ra""ll$< i€ forc sooae so'ler ?' --re <atetr '- l< a'fu'€& o..^. 616en""[^e- "$ " it ' 6 soi& *#* e- -ieen'eer '$ +'aoni*zedYdi%f' y 4W" -o{,- rrt yJ -- A , t:'Lerr< -T ' i s ad 'nv ]ae+i+.1'^-lni,<9 '/ rs i ,""T*f ls *t* TL€- ou'no'"ewlte r"^<$'r< o+ J l*. ,*F,.*l*6Ltd +t"q I ot^-r,oeJe*+e ?.+.i^ ol ;', -ru - p ls c. ' ', ijrr.. ;!'"i,.- r;-, f.!6""r" q^[ is ? g i. .1'ttJ +". et.nae],ts]lc er,',*,"(.J *l:; ",^*t,i"ttt*1.,*,,trA1e€r.rs" . -,,-kn^ es*."dr. 1$J...::,,
  • 98. **"ki I I I ." !. ll s oa{(ecl tia< . l+q< sii<rt,: ,l- n- or^t(o-e{ecs$. €4J4SSo/ I a, r, - .:r, ..r a'. Icqq vgertc.. 7= 9i *..,,- , .lL I I T n p$4rvr"r"J .t' .aY"dio .t-r -t-- " )"41, o- 1,f 'r t_^AI= Iu ')| Q -:9 o =9r''"; ' " ''-'' -,'r- .;Q"-9u=a '' ,i-.. ,1 --. Li e,"e..r,e&+e.5h" .
  • 99. d5, a9 !a- c?E - )tl L ol ^".1U'J vec,FrL &rLley* 3 ir,Q --'{..' 4lae eigcn rnalg^e all elge'dl,{e e Yha1trtt(- _ .A ' '',>+.:.,,.':. dl^q Q5tfr'.'*=' Tq- s: I '...01-+ | -r' L-: -.: .J. & .lr aTnl Fi' + 1. # i.. , 4.=7-t-+ I f " < I ,--,1o-'.^) :. La -s r€ et '{leefec6h e *+nlt , 4 l-r o t 1dl - / | a t'e |o ? i "4"- -t=
  • 100. IL.J t I ! f { { t .i r.y- ,i..- - - ^q c I "v.cJer.gF c q)'j4t1v'' - 'r1 -r;o -r|"< L"S,1€ =lr'- nl ;) -s= (l- t )1U>n"t; (',:-t) . " I *l('- :*" - -'l' ' '1^--F-I-t rj"o <a^+5/. - /r-i l'r- 1)l % L) - ' // ! // "/ td "fke l+x i ^. .1(? Ll (rrL)'o , r-7' -' ' - *- 1 ,2, D'- . [=' *l €i?e^.6eto(r := I ;".,l -****g r o."g "l "^!a3e^..et$n w,Lre ? r+ - ^ 1.^ ,"1Ut -9x=" aa rwn -lnivia-[ s'4u"
  • 101. a L:ie r.,I gq.. -l =[ - 12 +^J 5{.i-- "J Sslo""' "I a o a :& (. 4in er.G x,_t- f,J=)ol .^ra
  • 102. LeJ- +1"e" "al^e cj. -- c"a +9 . rr.< e-laer,ve<il0n d 6 o.$rtro6ai"Si? -lo +e 7r ze(i, v<rftRr oJ€-lfrwsuq, 1e= I .^---' lal. I r - | {r€ -1!Itr"1 o I L o)
  • 103. --, ,!-' x"h'+-tq .- z- .=0t.. l -.e-t.L tar"4_ aaet.anic.lotq {" -c f4.+;)2 'J-'- t/L4,L [ +.'' * z_ tfrJ'; 1"..' I o l-).1 I s -qe I lol ) ^) t*-t^ert T---.-^.Ar!^"b."e^ g.}i' ;'' ."-i'' f-: ?- r-l fx, 'l 1"1 Lz i z)l:t)=lt). :' -1
  • 104. .!r,rec-yt equ&rr -:x1 - 1r<zl-! : o gtr-- 1 - d Jr.""'.-i"$<|:e t^4€_ * -9a- 1r'<e+o cnil p"t8 + {<."9o" le! 2=t^a1o) t'+ o T-t,-'alsi - rt -_ -4 t l') *' '' '+ l?-:*'= nr-s" L --) -j = i1: 1 __ : = .2"- " r , .-,^--o-vr'&"E l' lk' -lfa eage.rxcL'R :f - *''."'- d -<"'^ lutt.a.-.. + T' 'u ^" Y1@^k*d . | -. f n/' i r..{"*1 oi 'iq +o-, x = I 'a.V"l .l L1 -1 L t"l t" rc,r,.e"Lq,.-_.1 .fle. t'.-- li | '' 1ts1.,e -- -')