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
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
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
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'
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"",
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
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
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"$.
,^g il
sir-plor-c
a
il -8
r@r:l( G o| Jt'e r'"{tdx +
"t
r.r^- 2€@ lloos
O )e+q!Y^ina -ti.e *o-r' "l
r'.trrr( A
L
-11
.l
,l
;l
I
ls -ll'-e
"o{r.i^
+
'51e.
rA 1
,Qs-l r a
I
:
Ll tr
cd€ Re
96. I tr,
I
+ I r _.(
l-
1 I z" R -1
^ =/' -Z -+
-r o- 1i '+
t- - {
.1
-.1
o
o
I
l-
a
o
o
o
1
o
0
o
0
o -.- r ',2
)
r T-'.K ,9 **{ni"- = f
97. '1x, -h.en
{.,'=q,,ar. -:.ra""ll$<
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"
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 -- -')