• '" ., di.II �'"'1 t .

, fchclon r-�
llAta:.ig dlC' g,,_
Yhrao fnon n
he l':11\korlhc
�.. Ibo 'Ill
'1 o 1111 "I'
�-
ranL flbe =-u rows Ill Uuit tJi � lt�I
1) �... � tit.,
the h,-,
.,

Ill lhc � '

� 11:Wru. '
x. Jlic,noof �
P"C'5 1hc � ind """'so,
,...,
R-- __
rank of lhc rn.ttrL-.. • CJ!cnder.1 ro� o ��
u� ll1liD O.n.on r
6.
ucal &t,n, •, ,. ,, ,.
f""md lbt ,1lue of 1t.r rotlo.-lnc drtcrnuaaat1

l' ,, I'
ll.J or (I, OJ or I 1 0
2 4

l
2' 4'
0J 01 0 01 • r cknote. l c
I'
•• l' l'
I (I)

ldcm1fl n:atn., Ih a , Onkr h Otdc,

.,
41

t of Sol�tion.
at'-
The S) uem of linc:u �:.:.: he raru. th e g,-eza 111,__
A.'\: b • -"- I l V 4
as saxf lo be COllSmmJ Ld A• l' 34 4I' I'
2'
Ir p(A} - p I A �•I
-1: ·�,
b), P - nm. 111d 4' I' 2
mconsisrenr if P<A) .. P (A
b)
for IDCOnsmmt sy stc-m solu
tion docs not eiust· F
4 9
S) "Jlcn 50lut10n �,,s-.s and or rl"lnsiaau lb I
umque Soh1 11on·
'I 16
p(A) • "lA bj • ,16 I 4
no ofuru:rnmnstvanablc
ff p (AJ • p {A bj no of� s
n variables Appl}mg C 1 •• C 1 • C1 + C, t C.
the constant S) stem h:i.s mfirutc solutions :JO 4 9 II>
. • lO 'I 16 I
lmcrsemetbod X•A 1b• �J b 30 16 I 4 I
(Af ., 0. JO I 4 9
8
IAf ,
9 To calculate eigcn ,alucs }. Ta�ing )0 common fonn C 1
Sohe tile ch:uactcnstic equation oflhe gtvl'n matrix I 4 'I 16
• JO I 'I 16 I 1
A, fA-jJ 0, for i. I 16 I 41
}. are the crgcn,alues of A I I 4 91
To c:beck an5\\CT add all '-and match with the SW! of 1hr Af'Plymg R,...,. R, R,. R, - K,
d onaJ clcmcnts of A lfboth ure equal )OU mre correct re<peetinl) \\• get
JO To a:ai� e,gm •K1«S make the m:stmc IA-Al)
Take someX,. 0 andmake{A -;.rJ X •O •301�ol0: -&
tl ; _\�,
-12
Putt,ng different 7 caku!ated bc(orc find d,ffmnt 3 -5 7
corrcspondmg X "' 0, !here are the eigenvectors ofA. El<p11nJm1 along C1
Note . To calculate c1gen vector X use trial or crOl3
mulup!Jcauon method I 7 -15\
• ,o 125 -& 12
..:3 -s -7
I I Dtagonaltuuon ofa mattill A
Step- I Fmd etgen ,aluc:3 of A Arpt)1t1gC, ►C',+l',
Step. 2
-• 3
rmd
malc
called modal matrix
eigenvector, of A
e a

.f Calculate C
mat rix C of the c1genvcctors. lhc Jlllll
lt 15

i
t'1�
• 30 Ill � 7 j
'I DJ.in� Ill common from C,
_:;1
rnam• " jd
1

c AC th1 1 1s the dia gonal