Kod Kursus (JIM 201)

Nama Kursus (LINEAR ALGEBRA)

Academic Session 2014/2015

Kod Tugasan (JIM 201 TG2)

Name FAUZLIAH BINTI MOHD SALEH

Matric No. JG/6761/13

IC No. 871102-02-5350

Regional Centre PULAU PINANG

Phone No. House :

H/P: 013-9490026

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t) Pan k c0) + Th e raoY crl tte rno{v-i x t, q ,I r *he

hury,b Qrt' leod, n+ errt", <.S

is *hc

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--- [1,1ri,] -oJJ",9l-,--t-rzf ,!o-,]r* -],t] , ct,\ ,L-,r-,-ql

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"trao lc 6+ B=t|

c€ "+ s ; q.d "./e

\b

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(\4ll p-ct5-{t :zEg(4L$ - ts{'c€fg€a1- g+" ?<!$f lseeEq-!.^*

lEe tt4e9-'* 9s-g=L-=ssisn +!q3- \o)l ' YloEra -r1y drnomal:

s-94 go og -!c69^def -se-.rq,=11!-eo ! c: llneov\1 Jeg-+ncl"n*)

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wv E\-&- veEiq!>,r J..\'n.., rvq|€} r-=e{o r Vr

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s<o+e 9-vvvgz3 ta-r3'- W

b?-V tflh -9+bvy^9! gao-g-lt1!eq'--\ b^$-) W- 4'og -*en4:OJ'ngl

\& v wr, .--,. -, .ul,{--, &n3lt* --qY-rJ bz'hegrg e.^t,rr.n3 lofi B:!]3

ne3=4:!$l - -wr,-4':--' '-{4 *f€+ \1C$:d*n$,!

nq -fhg sel q-L,&,*t/tr, -... -W-'f -&{qv q basrz

Eace V,

f ,E= N- i=!zh - SP-=c--o9 l-!rz!3 resElg.r J,an J= t<.+ rerlej 4eFt -w, l-q!e -9

J.,oor.o't qges

eg=s<i 1"ag- !-e,r!91l+ -d:Psqg\'

q) - 3 q{-\.\ +G! -b--"l-*ldtr-- se-<{9

b)_S -lgIei l'-,qg w

w.3 T-\.h

b=g-t iv -:'Ee

\ineoC

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rFo

yne(eO

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k i,rot<htt zn vets-Lor {<z

I

€vm*€ whe\he,r titnf {rv€fr vec*o{S-V<\o'o *ire \roeef\\ -Je*eoden\

= ( 2, I ,r1) V, " C:, -?,5) . rll -- CS, -.),9)- , rlq = C.t ,''u;-l)

OrVr + q>V> + 4rVa + q'+VT = o

'll '1, '/,t/3 n,'hLtt

:-l

\ 'b ull '[)-\kr+haellr alt 7z '[to _t,/a _u /l ,,/r0 -ub -r'h u ll

I0

, '[z tl, '1,-tl? Po + b3 +R3r al1 7z '[,

o 1l; 'L - 1/3

'- 1-',*- "--r "9-.-.-**l i1 ' :: i', .--.

be, *:2e> +5aa +- E4

A, - 7q> - )qr -r \Qq,,-:i:o;-

Yqr + ,9Q'> +'9qa 1

I---+--

1lz tll -' lt

-br t 0:

+Br

-3/rr R.

-t P:

-% P"

+ R+Pr

hoO 1€(ro

a{< l,n.oo oJ.n{ ro P 3

?+ Aq."-:i!Et!€r or ^ot +he €--\\s.-rE _e{e_ $r,_q t pe{"_stl i

!_<_q-__V_);_-7trrU r -t t - >U>Vz

4c^ ,rl ) = Ju,Vr + 1.2 U:V.:-

/ V rrlT = -l q,1 + t.2u: ), o

kt U,= O ,Ur =o .: -r co) t t'a cs) = o

ott& &.'{ c.o n4'.Son o.8 \rrne{r ,p.13d..*'

D ZV.u) = J v,vr + t.a V: vetYrr? - rurvl +. -nJ g,V_rl__!

= Ju,q.tr * 1y,q;, + l.2U)\)> + t-:tJ:VJr

= 7U,u.lr + l'1U>W- + -'lVrr,tlr t t-:VrU;za";l , t,, €, -*- , --", ,l/ .w_--zgi-!zV--g- (n V

Ccu rv)

= ( (f rVr -t t -> \tr-V>)

v) .fon t1r\ rn V ond C -a fcol Atolcr'

ll) Z u,v> = - -lUrVr i.) U:Vr./u rv 7 - -J q, u,

= - -1 co) \'>co)

s n.t sa{.s{q +h< c.nd,-lioo o4 \ h€ Gvs{ tnner__ de.s n+ _ge$jgt +h<..+ .

: JU,U, - t->U+U-zJu,) - t-) uj

ZY, U) JVrU, --l--)V>U:CvrU) cvru)

c) (u+V zw) = [.rur'ts,>w,l=

rlil )

f.,-, u> + v> )W>

= fc-lu, \i, * -lv,w,)] -fttt2U>$rr) + t-) V)W:.)

lu,urr - l.)qlw> + ?vrwr - l-: v: uJr

,_dL (S!_zU) _:-_1c_gl_* V, - L-q> V:

= c (-lurVr t-.f, q.V-)

C a re-\ g'(-o\.'a'

(*rY-tG)4t=9t

' fl.>= *<

:tq + "'t-b =b

t*.r = 4+b.)q =-?b

t. €\P

4= -Bb qSqrvn<. L = t

Q= -z 1'+ l,: A- -3

2{c + 3{J :6,:*- c = - 3{J

c-- -? a a%tY. <-- A - li

L= Z \+

Theve-toie

f-

Il-.

H

when(

l'tj

ln

C + + *!,e \- P, +P) -+ P' -7"(-T---\D-ah

t=€\-)-2

-Zz(r * )x> =62d- > = zxt2 X, = z1

v>= { Xt= f3

cs) : s -,

-3

2Cr t >L> --oL2 Cr

gf oq-7

-7

c0 >)

4v (n') --o

>Cr> + :C7 c.,

t- 2 Crr>

C,'=

Ct = -? C>-

(c,

+?es -+

,-

--!le+< !*) :

l

[--

.3\-7 I ---z-J\$,"-S?

No.

D:r le

er'dev l&e {",otroq T ctlt) =

> F.L >xP +aP wh<vc lar Ts avt

Ett" &-",d lLc .,ix'g o{J'r 2lnt+B

lcrn) =o i\e+ rYr = I b,, t,.,

btt b,z

3k9 | [b,, b,,abt + 7b,>' Ybt>

brt * )b>r lt,>',+ ab>>

2brr { Zb,,? b>, ;7'b> z

-b,, -zba1'-: ?Vr> (\-tc)brz + >br>

btr - 7b>2 C7 -u) V.-

-L) b>, =6 . (l-k) br>::F )b>>=o(t'- !t) b,, = O

bcr -Zbt>=obr, = 7 cc>) >lrr, | ?b,> ="o

Ylzz -- o -Lzr1 -t o - o =-o

rnd *lne vq\.reJ t4 coos\ortf 1 sq( L *t^q* +{n< rvrcrt'rl r

is \nvey4.t,\e

Y 3*)( II -t)

-) 6 + 1lE -)

o 3-) \ o

=r-) ( -).3-\)= r-) ( -?b +|') -r 1 c -\ I)=*?I-r)'+3)1-)3-8>

)=o , l-2 =o )-) =o),=1

-)) +q.. It + s)

_\ -so

9Y

L

=*4( lo) t >c>o)

'aFu/'/

r\l l.

6

3

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I

I

2

b

\

:

l-I1

-+ g- g

:r- o

f!rydil-S \s no", rnver{oLte X__

l2 on a\ mo{; r D

g*u.+ s= Pof"-

., d afl tnv elr L bte v)

$ -u

i .:( -l - rr)det-ro +2I -s) +>) t la

= >,--7b +az C ) z) c

)- I) - > --o) ='t

-gtsilgia{)=2- q 12

-t 7

-Vr + ?V> = o

Vr ? 3 Vr

-Vr + tlV, =o

pAp : P*t P DP-:I

-Rr -t E, + F, 'lz o

-'lz I

-3 P, -, P.

L;) lz- r/,

-f l, P' -t Et -r P,

L,

9

-?

r ult \'/, oIo t f \ -3

.lr

-l) + )o

-28 ?TLt -3 t

= \-c +g -g tg?* c-z) q+(-3J

-\ 2_ O-l-; '

.-.

--l

__4-g_!d_ylg=* o _s4_gt sosn-<.q -r--s-r;:p'LL J'g-'-gsrq\snr-

;r.$n.d ==-

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eJ

r+R c N,d \n€

hatAs of &,1s'l

Cd+

1a" aaa fn6 tn l,\l a Eco\ocS X -ld-l4s

g

ix

g'eolcr

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ta( + DA(e( * b) br z

cd=l dq I

dc o(d

e{* he.d g^1e e\ +a h+ h..nJ grJ. (" +t^= t rlA holdJ-----a

( *+BA) = +tjE

lD Del-errnin< *\n

Vr = >-Xer)e r a- n( .-Il+)?( )x+ 3"(

L'-fI

i

Vr = \ ],l.t(LVe = q-zx43z(->

4qV, + Q.t V> -t'Cl.rVa = V

V = q2L2 + brt 1C

, q,C2 -?() -h q) ( I -+ ,7{L) + 9s C Yrl-r( + 3xa) = v)z,9Qr -q,2( + q> + 2.a>* t \qa -)QzL -t ?Qt%-> =-\,/

:Tarx' * 7Qz2L> o,9( .'- LQg"( + 2qr * Q> + \+q s = V')

: C 2e>- + Zez)z-L * C- Qr:- >Qz)K + C2ar *er --l

-, st-:y4 tc.

2q>+2A>=ct

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hr-[i- o ,'[-;---1, , I [r-1o r olru+.

-2Pr +[+

T

77!

%b

f--

;-

f

e)l,en *h"fS q &,ts ce o* F-3'

U +V

a-b

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c=q-bj

c.u

b, +b,cQ, *a>) - Cbr *b.) k

Qr + 4a

br + U)2

(or -b,) + (q> -tr)

4, -tor

C Q, - cbr% S ;< subshac< 6 $ tp 3

il> t,,a q

q1]:tz\ -e Pt is Jefin.J qs frilo.op r

74t *n(>+1(g + 2r(+

Wstf Pr.' tt^e V€w<l "+ T.U,ta+ + +{n< u*-t7

: '--- --- -1 9aLt 'a?__t a-g + )'(t

qt+ '/(L - leZ +zL,a =6

-2I

o

o

-22

I

-l -2

el, 31s

7

Er #) P.

-2t

zzQS+Ps

vlv

'Y/u

p3+hr

hE

]

rtI

urh.+ Is $h" G{tk-.+ T 7r<+tl32::ar-* 7(*7

Z2Lz?%

q bag,X .lrrv t{n.: (ro' *;;t--

ld'-2x>-l ;, *o, -

il) Eqd\ '[ 4,'

*

s *,tt

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. f rrlr txr.{+ + Fe'Ig l]!t r,+ =

_o_ __ 1s !!_1,&,.gs ,lCr__=6

t\< $sb.-Z t1+e\-1 E!=:< Ts , n1y1{-\e"+ -bJh= {r\\"-o,h9n^o3<n39n-s q;!s{. * o+_a1*g\\oSft"_r- rraG $oir)!'!19€= +1^€ ve4-ztrg .+ ?1s _ rs 3(h!tqlj -! = c_et_.+: al:_!

-a4 qq! {:!^< ray:$el- +- <x+1< ss u! q< 4 lrlr--r,,6$ y<elre !n- tL_r q"+_f

= t V, ,\r, Vg , Ll-v\ = c]! /rr)! f_ _L|Yrlya* (1/rr)v3

A

the c4rE _-+ \ = 3drtn ens'.roo oQ

-l

hg. .+ T-+h<

6n€ le on< - ah.n .? C,v< 6 'tReg rl

f d.nS6€r

oo< -*o - oo€, +Drr "S-.rrs.-|r-6r

Sroes l.e rne I

:

\V) I< T oofa ? Ctv< q ccqson Sr $oqr :!qg!r

d.m (ro,r',q€ T )' = Zlrm (f-tq€ T )' = Z =: drsenstoo B ;

b Dete"rrrinz 4', ns$rtot, on is ltneo r

, u : h a"r -+ p' erc\t .rrhat L { a U\ :-lSt-br1.-}4-t31 a2!l

W Ts c.-\\ed o\ \,r--" {caog e.,c*o\t t -4 v ,rt}o

q) L Ct-t*V): KU) + LCV) 4or <\revq U -t V tn V

iur) Lcch) = cL (u) t-ar anq u ryr V qnd c gq-c":!-rybQ{

iL /q b\ = Cq{b+c t4 +ee+"{

u) L.cu +v) -

v.' V6

Ua tVg Uq *VsUr {V1 11, t t/r

Ur +Vs *Vg

- (,1, * V,) * cu> rv, + cusr va 2(U\i *V\) + ! CUs + ris) tlCUa*Ue)

=. (q f b+c zd -t ze + r.P)

I Ltu) + Lcv) Vr

Vs- Ve

1 (lr, "* U3,, , Vr tVz tUg2,Uq *)Us { }U6 ;lVr.+ )UE -t 2V6

f{ql_b_t tlE_+ \r,llf. t !a ; r('t * lus t\: rfs !}ld=(CU't vr) * (ur-tv>-)t Cur*rlg) , aCuq*v.r) + a(Us tvs) * :Cgr-t uC)

= (cu, * cu> + cug 2cuq { rcus + 2cuq)

Cu,

cug

C(rv cuc

r +ul 2Uq + aqs { }LtG)

: cL Cq)

to, L is \ r r,c a c *rc of (trmah>n

66 c.o<rrt"y_:t\. drl__t_:

r) {a"'d *tre_ <rgenv.,l.r€s 5Q _A_C)f -.h) =ode+ (^I --*) =o

Io

o

.) +r 2

)tz

de{- c Al -n))tr ci) )+:

)+t -t

)+r

) t t l()+2, It z) - c-: - r1

e}:t D-C-b - * z tr + g ) t e =3)-+ 6-r

^) +t))+1^ trf

-r c)+r) cX+r)ctrt+))+ I = o )+q=6) =-l

.<gcu=Igtt = -t I -\F >il_

nA all *he eD e0 tce ,ra--t 4

)+>

) ---r

l--- C- >r(>) + >r(>= o

Y.->

1(2,

.-o

I

la(t :I :2Zz a-r' * !il>- = 6

lt*O=O

o0-f

= --Y

-a

-24t t)il> +

- 1", z

-L?/l, 1 ib 't ?73 : o

4, -a> =o -'ll, -ao =o -29(t * ,r(L + ?A 3 >d4 -- - Jly -(4>) -il> zoe O-+ o +3ZL=- o

i=-l

414LX>=o-,X, *2Q(> = o;2A-r * 1(>=d

2A>*2Xz--A ,,, *r= o i

^l

=O 4(>= O

n(9= O

92(z =o

--UD-g S -QlyS- "

feq8on4r€o"rr-onsurej

'-f-; 2 o

e\ sen,ro\.res {l--:re M-LJr *=- Y---vs *{{o,,/ "A +e nU < c*o{

__ 1,: 0 J(r = 0 / Tr: o

o o o

0 0 d

€c, fh<.e-1

o o o f< \rY<crr rnl'e

o 0 o go $ <of) be

0 0 0

\v) Frrcl Vzasl 4, v €'3:l--_1p "l€ co ( r'< s-Ed:fg--{' *l"e-

- \"gS4- <i3e n rr.\., e a{ -S

\ = -t

L{srq4:n+ -q"vlql--Jio.ro ooh'.4'

--\J-

> +>

-\

-2

)*t -2

4(+ -- o

4t4\r:)d,=@*Nt

= ->4;' = Q

-2r(> - >z(1 :e

-\tr>--o

s.a -=!!lbr cssa-=!. qd e--]

:]-- 2 gl'- -I -? oE_-) -r -, lt

12> + P1

)1,- -Y;

_'1, OO-'6P, +h

-h, * bl -+P

o loo ot

o

E.h

_tr,-t/r

Y.

-,/, o

--'4 _ -'r;

t6

o

_q

*t

t_ _!o _l0r

+-Pz+ h

)-to'

-)/+ -' /, o

-t/* -'/z o

's/v 't/z

n)lIn)lv '1, o

t/.-' \+'1:- ot/, ) *{

i I*t I )'+ )/.r '1,) +'1,

iltr l()'+t *'/r) - ('1,

)'tal

)' t ;/rr tr + '/"I + 2

'\> + v{ ' t t/t +'le + )', l/u A * r/rA * 'ls!

+

* q/.r I2 t

iq)3 +QI'+6) -t t

icr; ( )+t h *t ) ) *'/n)

)+t --o t/* = ,,

l =-l

3 7 7

* bas;9 r *he nr ll

*)P*..* Ps + I

i 4t + 24> + Qz +1!7te + 9?ts =ong + 1+ + 1G =O

4Q +2(t + Rs =o*r= -%V -X,

+2rt> + dz +YL'+' r-44's:--9

= -?*> -'L> = ?A.r - Srt.:s

= -7q -c-b-c) -2c. b) 5cc)

= - De +b+c -ab -.S<*2q -b -*e

*:,+

-2-a -b-+c

: -b -e: i-

c .: Ll,

i.i Thc n'[[-

basB

Vae"a)' "+ 6 ct, i)2^l:

-\B

Ct

ce9

(o

c^a t.rmO

6bci)srA "+

-i E.+

i- P- + Es: +Ps

E' x -- o

Xt = o

* 24t -+ D2 l' Pz

- Pr'-t Vz +2P, + P1 = Pg

- fPr '+ h.:s + Ps

q

0

hr <* P3

90

= --2

l.=t Xa = p-

4tE

Xr -+ )Xg + 3X(r =- -)Ye ^ 3X

z.lD