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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-
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!.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
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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,..
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-"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
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nt i* tiz +an<
l,
^r,.,t el,evvalgs.s,,
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Et' a,
Li Ske't sym-ujri< :"no,l,-rix'A >r+,+re ,natt; * t+ , nAted
/..-''----....-/-'--"....--^-^
9l1ew-.symp2trie To|aix , )L
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h) Atl.l,qo"*|" o-lzn"znl.^, a."<. z,1.,vo.
OR
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h b,f
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g"r 1Al =l L 2J
' L3 4)zrt
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ll,terrhon;< *l'e row,s qd *U
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L-L --o l:he].^h b' a Sing"J*
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colu',tt4 )lnto ttt z i* ."U'zd *hz l."apo""< o,E
t
3
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17. Uni1".ry r)o"tr)t ', 4
/'_---'^------ A ,,,t -.ta'd
tp b€. |.tll*o.Py- ,l Ae4
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o 7 |
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=fi.L"
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oli o 1loytna)
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Lt. Ccr:lcratz ah- tno,t:.ix .. LJ
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-1
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t eo,npi,ott number . -6* cc,mplax :"omi<-rn o-+6i and c_6j,
o- alrd b re-{
I'un, tU", cor)4qyatc
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--__----__,-
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4 *
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br col,XvJuzt
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We.t - hzrh+k^t1 t,r_fi,.rz o^<
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o b t.Lt t. a. h .
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aU JaW &.aq1:lna.!.etznwlz
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^-- lz -t +1
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t' -L -3 I
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-.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
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oa?e Lwo .>"6an'e, tn ql1.r.z^ o), th<
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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,,
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..---_-----,.-{,-,-''r.----'.--^'-J,il
^io|
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q'fr1.dy )n ^Pou/^
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rt'. lAl{a ,lhzn A A a- Na1- 44*utot hdtD tz).
non- in4oz
be i*;-> .
afun a 51r.ore-mati* n"t )nv
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A snytat'< ''habiL" A' *o
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f,z l,n,t<n* ok B a4 n =g) .n'eY+e
fi.ve4
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tg.3h A_lr -t 6l
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= I(o- o) + ) ta-
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t ol
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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
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w hare
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be o.n
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y'6duxt nB, i: h'en ,1how *hJ (he) =s'a'
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9;,ntz, pB h *, *rp rnJ.r^r.
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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
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ve *ht
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erJ
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fpro v
kno*
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fn')
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te
ho,
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-n;L'rir-
can be,
/'<
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€
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
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e o, ott") ,. .
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c =+ (A,A,)
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xy,"n2t'r) a
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Srch tJ, g -
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p
t
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p-+(na*/)
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(A-A/) "1-t(h
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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
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a.
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n)=p- e
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o
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ti
G;u., T,n
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a
tlo
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o
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Co-bocLor.ts A,4c
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lr::l
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ll I /
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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
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1tn co,!cu,la1=-
Ya-? B' B
G)""n
w(s;, L
.*'I,h
l7l2
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c)
a
7
2
()
:l -tz:1.1,.
:l -li:l-li:l
l
il -1",:l"li:l
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D
zC>-")
B;B'-
1 o 'to +
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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
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ts9
.E Fi,d t)."e v^luu, 4hd2a- v 7
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t
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k'
/ *-z -r z),
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$;ve thott
l-r-, -"-.)
V-r e+z/
i)
5o,l!',
@
@
q. gd,,@
-7
-z
/r.tdr 40
-7-
-2*
-*
-.57
LT
-7
Hene,wz ye*..,
.1/ -? =
a't}" C X-7)
7-t = Lng
aLt=2
- l 1 ,--
€+? . 7,y
= 3- 1.
/T
.? @f
*" t"j,
y 7
--i
2r-G3)=
i=1 et.@)aan J
3-1
-( )tt
!4
1.
tl
^L
2L+3 =2
.t- L
guJ ry x=-L ar.rd Z -
-3 )n e{
C + (-3) -_-L -y
_=23 =,a_!
eY=-3-1
A-n,,',z -,_ L, y= ,4- ,Z z 4 & *=
@Jb o.[". ,] o,d_s fo
LJ 1] L'
Aho,.t )',"+ /n, o,t,, , 4) (p B) _J
",
-,t,
' -f
-'>r' / t,nLv?tr .f4":rt -/_
o l: ,l B l" 1l
Lr 1l
lt .l
Now,r' 8-1" tl-lo sr
t t't -l
L' rl l'ol-J
- ta I l
I -l
L2 )l
:l :l
,, (a+B) (A B)
L:A-e. f o
Ll
'LZ
,',@-te)(n ",1
1
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.',-[Z:]L:
- fo* o o+
L.-, o+
-Lz
=Lt
ta 1l
la ol
f^.-
- lY 't'
LJO]
-
| o +1- |
^.
-lo.)l
I a 1l
Io l lla
l1 )ll1
Now,
^L
h =A A =
:l
::;l
:l
ond_,
B-=.B,B
o* o )
, * oJ
o--t-' l:L- :l'J-f.2 I lo
"l
=
f:
''(A-B) [A-B)1P'B'/)
"L
l:
t:
I " zet-11.9
Z
L
J
o")
. Srnvulot olt I
I
L
=1(t-*)l
+
z
-+
3-
-C,,I'i
2
+-/
-+
3-t z
2 +n
) l-9 +a-
LPtt"'et
'o-lnz
"5 I , lt-
-J-:
o
-ta*L/
ap /
2
L
=o
-
G-t) Ltr-3,()++t
2 3tt- 9*-zi-t3zL=
=)-ti + Lz.a - g tt --o
.=>
-/L L/,--6t+1)--d
7Q-,t) l-* +x -+r' * tLr+4) - 2
a )L ('xz 2 t 3+jL). o
( t-s)---o
)L= O Af
(: zt)+7G
o
(-Y ="
+ )L-3=o
[=un
A^
/Sa
yaXtire:). v o-[tu, oh- tuAr3*no*.;L
inylar'
i.,r-zcir- equ oj;on
,A-A^^ :
S,l'ove *l'?, ka"Llowiny zy+Lem ob hr,eqv
ecyro.liair,rb .",,'L L^< Mp o)- .^oLr;x:
zx - 3y -r'9-z-L
?x t+Y -tz --to
r .17.2?.J
lZoogl
t* Gi,en hh"J.,
21 3y ++z --L
3/ ++y -52
-Lo
tf - VY -rLz -- 3
e.tnoJjonf ,n;tv'z-u'-nJ x J'a?r a'Pe
6eLow ',
'Te given
"/rrtte)1 04
Con4iden
to,l
Ax--$
.',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 )
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^- -t "t,
(e+e)
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L
r+1
J
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l,t
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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-
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'"' 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)
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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 -- -')