lecture 11 econ
DESCRIPTION
EconTRANSCRIPT
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4.
Rdevatnk Seth.e^s herr\ re-x't :
Oefanvrrv nrul5 OF oRDER 2
Ttv d..e*t*mtntu'L o & 2r>
dunp'nts
EXAM pLEs
( , ) A = ) h t =
(2) B = fB l =
DETER,M'NANrS &'N_vE86E MAI{ l , t+E9C HA PTE R, '16
t 6u6 t t6-6l b " l ) l b , ' Z t
i
z &t, Qzz- CLtr&rt
( L )
(ir)( i i . l
(3) c .:
1g,, a"iv It Qzt Qzvl
\ r, "6\
Ict =
.gYgrenn or urrvnR gQunrroryE r,. rAE CgnnneRs RUIE
Cnneider +t,q ft1tanr,^3 St*^ c:onoish;^, "f tur?linear epfr^oJdfr.ns ,
'
a i , t1 t &n \zQz t a ' t + A "a
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TIM, rn-cfrfiititt'v* , Tla,*rix of +^iA ry aystorn a(uygfu>ns ,.t^ SLtN/n W i
Tv\!, u,rhL,Q, $rfr
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(5) To sotva {on xt , x4laca cr.tvm,fleo- efrffv;ur-nt rnaL*x wv&. t!r* veciorb ) *o rmtag a, ^erD matalx A r
A t : ( ! '\ b ,
(4) ff..',r/- t!^L delrrrni,no/.^t o A, :
b t & ,v l = b ,a r - -b , .&2 ,b L e.7y) ^
! o tr^-oP @ns{su&g
6t
(8) h?pQ
lA r [ =
Trv" {or. molu
X ' 1 = l
lazl =
hr Crorme:'s wJl- rA :
l3: ?:,1 =Lr@zz - b,ew(A l . t &r t Q 22- Qtzezt
ulurnn z sf fl^X^b vec.tor ofmafr't>. AL
o p A 2 i
0.u4.2-1
,ttle i5 :
t u , , b r - & r rb tO r r Q z L - 6 q 2 Q > l
l',16r
l * , ,I Qzt%2
( ^ l
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,sls+offi oP equah,'o^s o%3
Ltq3 2
@
=r -36 = L lq
= 4s = sq
2ol =
&o
q q 53Z t-l
1Il5
l " v lqq3z 6r(o):' 0,+q(,
(e;ctlT- G)u;)
2 . DETSRM INANT,S d ORDER 3
Conoldet Kg mu|.r,ix 1+t\e
WAn
futto,*g 3
A =
To fnd-+l,w *opu
detep-'na-v& oP ahtvw no&,,;x , {ofte",beJow ,'
t fd(!, il^. k\At derr",e,rrL of fu6t fDw &y1 arrrd,*u A't r@u) aM^n J,n,(g16 . Tl\!.,n mul+*pe ey W A^_of W Wg' dlerrr.,entsi
Qqtr*')-@@il
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3.
"l
T}J,a V,o ,*ug^d de'mer,,* of M &v eiz, ffilumn ),n
'fdIL W ttrild derner^P r
ddete +tw ruD a"d rclurn
beJow tI
lA l = tu t t l a * an l r &ng- ) !a , , a r r l1a6 la , ,e , ,I 43, aetl I as Qgz I I au ezz
= Qy (azzQzs- QzsCtt)- &o(Aoqzs-ez3Az)&n (ay Qg, - Ag16oz)
ETnMPLE
deterrUo"rJtt, of +'re {otle :''.;2 f}x)Fdm{t Vrq,rnahix :
A =
e
:
s ( ,2-7) . - s ( ts4q)a-G\ * 3( - r : ) +
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5. M,NoRg w cocaCraRS t
Tho eleonut^ts of a- rnaJb&K *t rnar>ntrne aFfe*+lt b ddejn"an ru ceAt oA dewLbtd o&u.,,e,(prn a aubit*e:,n,ndn^t of & ma-ttix eoJh^d11"!' fr.!I:l0l.'. Thus u rnunor I M,defer^va,,* of tl^b Svbn&tti o, ++W, i+t* rou a."r& jt0- qtornn + A^E.g r let us @r&vu ,riW- ; @xay ,''a$.ix
I
It 4 u = I ? r , o u l ) M , r = 1 a , ,l Q g r - e B I
' l q t ,
A cO(qC*Or I C+il 't, tu rnLoOr ,tt,.it" U,s prusc:ik{6qn : Tkv ru(o" Sr &.L 6qn o( o'6ocJor
'is a/)
?oftou,,s : .v ,aj = (,)'rJ t u,1il
J o l 1 u I = e r ) ' * ' / V , , 1 = l M , , l
lC , , I = F , ) ' * ' lM, r i = lM, , l
I C , t l = e , ) ' * t l M , g l = l M , : lI bFACTOR L.. ADtrOIru vnr*,rc;
rnqhix is a- najulLxis rcpbteA lrf L+6
,!n WhLci- Wprfgcnbdorlc; i l . -
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C =
Mali.ix Ad,1A-fho9
ihnnsposL s(
rnallLx. ,
I
F,xd"m0hir
r\-/ =
A e
' -z- .3
5
frl{owi,og rnat*.x A .-Gr'Ven t1lg
A^d fl,rp a{e."^tC
, l- l4 l
53
3I
q5
25
lg
I-{
fl; lLI
I
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(
1 \
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- _ - , L
Tt'v, fid:v)"+o ( c
v Ati A is il,* hn^spoto
A ) r * ^ lr r f l f i = v
5 . T!+E tNv A6E oF A MATRIx
f:pp61 +u,o*- d is a re,.L- nctrnbLr di,jtd,ru,*fl/s'^., o " Th,prt lb .r.l\L \s & u*IW" 11on 6d x-tCocLu 41^o* a.d,,-'rnvurce, O( c{ _ As u,x, k/rr,ci1u @,_a*, t v, rnafiix
r t^ W .LqfrFf nu_b*x I ',s
tt*- '
,ui+dpr"A o+ Lu im A"- r
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(zl -For wha* non'ber ' Q,/ -ie
rerse, o! *+ oIf,o"- if .'= ( l o \
\ o t /i -
' - , . ' ) ' \ .
' i
+ ( S u t o ' o - o \ - = ( , o \ , .\ 6 u - z o r t I \ o t / '
/ ; \ ' ' / \
) ( Q a o ) s ( t o \\ 6 a - z t J \ o t / .
+ 3o' = I + O. = t/2. r,!or 6a-z = o
- ' .
T,O der"NC flra 's6yqtgC- o+ & ma&,iX , @cr&., 4ua , et(ourahq &rm.ulO- .-1 ' u r
A'I'. = t , ad'1A: '
(at _,Tt\L tubow -t4pltu t!^o*. {.,4, i.rl\luw A elisEa l ' ' , [ A I + o l , ' : . , - , ' ' ,
' " , ' .
t',^rlOJ','eL OP fr". frltArr; g
To #"d fl^- inuorse t uJe, {ti,Lt nead 10 +i^dV^!, Qe)efun\ttatt*. f4 I
( A l = z Q r - " ) - b ( t 6 - D t q ( s - 3 ) = z o - . t s + z o: _ 6
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tz; I -ti ;t ll :l-E;l /t;l -{ r:lr . l , r f r t t r v l
L , = I ' h
l 3 q l t tI a r l 1 ; ' ,1 f??[. - 15
Ltrq
A4(A)
- J * q
3 J ,t l ts q
. _ul5tt5
5* l^ b
tAt
- L {{-l- l
t5
5
lgl r
64t,
Oa/,^ Oho,r.r- t
A A-I
To &t^e U*.fr>,d. UA u{artor
ft,An"SPoSA
tNa
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