Mth369:Dy=Determinants

I don't want to owephesne determinants to mnhbklhgie essential unanphke , bitty do he mflthwddpprks,so its usflto say a few wads dnt them

.

Tf AE Mattnd ,then detlA) is exatg

then1signed) n - diid volume f the box defend by the columns f A .

I } 9

>

at >*anti Tf A = too!:c) ,

th let IAI = abc

^^> >

ht : A = 120! ) .

Then let A) = 4

"

"

* ngArea tbaselheght) =2.2=4inat : A = ( at) .

Thu detht = ad - be

jb

,µ|µ'

q

Area =L at b) ( at d) tzac + tzbd + be +' zbdttac + bc)

Eattbftadtbdabtl-24 c

a b a d- bc

If we htnbe runs,tht drs th sin f the detnit .

The B exatfae film wltse parts ,th detrmitfdm

,& fllott delta B) =D'd HIM B)

.

Menem,THE : . dltl At = O

. The in f the witch to dins in less th n

. A is net innate .

In get , if Aemth ,. ) & At a i ;) & Aij is the srbmtxgin by ddetj in n & j

thUL

,th

ditlak Iz, thitiai ; Att Ai ;)

Far ayi

.

Et : outfits? ).tt#.l84lHttt22l4t6altHF33l4.81=15.9-6.8) -214. a- 7.61+3 1 as - 7. s )

T = - 3 + 12 - 9=0

expanding an fist raw

or

out ( iftg? )=p

1.ijt

'. y . 1831 H . IT

". 5. I 't} I + HY ? 6 . It's I = - 412.9 - 8. 3) +511 . g. a. 3) -6 (1.8-7.2)

= 24 - 60+36 = 0

expanding on 2nd rw

In general,sane runs will be better dries to expand on th olhs

.For exaple , if some nuts lob of zoos ,

thlj often a good rw to expand an .