linear algebra summary

l1o.trices c--,


0.11 :t.,,+-· · C\.,".::t,n -=- b1
°'ni,::CmI t- · · · O."'"Xr,,"-=- b,....,.
tL;~..,. e'j., l:k~~e~,: 'rf
'- l.e, Tr-i,ic.,.I (.i)
le
c.ll b =o
.s--l<d.;.,."
- i ,.;v;,._I ( "'~) ( ,n•rc._
(.J'4'f5 i....~ 5o/,.l i

'-'.'li<.~•": t'-n !!'l ! )
l


Pc..ro.metric: ·.


-0 Ir,+;" ;{;e. solkt,'o [) $ : a,.,.,, ::a
So\1..\.-i:.ions: ·. ~ -f-..=Hj 1. sdc.tion'. O.mn ~o


• ~ : !Jo S o\1.A.-t.D(')




-£.kme-ob::,,,r~ rf\o..tr;x :
.. k. R~ Kj M""'--1:.r;x ~ ,meal w\.ie.n
• l\ ,i, 0-) ¾· r ow ope-ro-.t:1ons a.re.
¾
r
• RJ·+ k R~ -:, yu- \'.or!Y'ecl -




:] l~ ~] ~]
°'- \:,. e:,
d b tc [ I o
e. -I> .
I c:. o I o
0
• 1-- 0 I 0 0 1
,t Ci;....
6co.'-'SS - ;r"'""'"'"
* low - ea-clo" l Redu..ce.J l. E-


Trot'\ ~QSC. : ( p..A.j '/ = ~;_, (_row5 I
cd ~,rnn s -s1.,;,k\...) <t ') 7 = (>..


Ti-o..ce. ·.




MC,\lri )( pc-oP e f l,es ·.
-'

, 1overse :




- A= =o ho-s 0 1\~ l.t1v1c..l .5o\\Aba r,
• - 11-.e. R.eclw:aJ - f:c.l,e\on tor lY\ e:, F A , s. TI\
- A i-s 0--f•e.5-S;b)e_ =S or=llAd ot elernenco.~ rnc,,t,ce_s
/1 ,O~ r~--
A= =6 15 Co f\'S15t-ent \j nx I tv\o..tr;"l( 6
- Ax := b '---.o..~ ~c...c6IJ 1. So lu. l:::;of"'\ \J nx , IY"la..t,;x 6




Do.~ono.l M°"br,'>s: : o.~=- 0 'v l1-j c~
0
o
ol_
0 O01
e .,i._.




• T,;~u\oJ t'\oi..b-ix : lower : °'-8 =0 \/ i<j
°'-\j=--0 '-dJ ~ ,.i.,
[°o
~i J~
:0 i:1
O




~ : M-u :: Je_~ [ ]
Cu: : (-,)'tJ M~


Theorems : · It A ~s row{ eciW1'0 cit le,ros => Jtl (Al :: CJ
• Je.l (A") -:; J~t (A\) ,.. Arw.n
. det (k A') :. k" dd. ( A)