Page 346 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math26-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs

B'N sK nkgD/^nkg d/ d[nkok ygs eo fbnk iKdk j? iK d{i/ T[d:'rK iK pkjoh y/soK d[nkok ygs
eo fbnk iKdk j?. wzfBnk pkjoh y/so s'A fJbktk T[d:'rK dh ;zfynk n j? ns/ T[d:'r i j?.
fi;dk e[ZbQ T[sgkdB x i j?. sK fBwB s[bBkswe ;koh j't/rhl

X 1 = X 11 + X 12 + X 13 + .... + X 1n + F 1
X 2 = X 21 + X 22 + X 23 + .... + X 2n + F 2
∴ X i = X i1 + X i2 + X i3 + .... + X in + F i
fiZE/ F ⇒ pkjoh y/so dh wzr
(B) ;zouBkswe ;wheoDL fJ; ;wheoD d/ fBowkD d/ bJh seBheh r[DKe dk ;jkok fbnk
iKdk j?. wzfBnk i ns/ j d/ d' T[d:'r jBL
T[d:'r ‘j’ ftZu ‘i’ dk seBheh r[DKe

X
Gkt a = i j
ij
X
j
Or X iy = a ij × X j .....(A)
fJZE/ a ij seBheh r[DKe j?.
T[go'es (A) ;wheoD ;zouBkswe ;wheoD ejkT[Adk j?. j[Dl s[bBkswe ;wheoD B{z
;zouBkswe ;wheoD ftZu gfotosB eoB s/,
X 1 = a 11 X 1 + a 12 X 2 + a 13 X 3 + ...... + a in X n + F 1
X 2 = a 21 X 1 + a 22 X 2 + a 23 X 3 + ...... + a 2n X n + F 2
...................................................................
...................................................................
X i = a i1 X 1 + a i2 X 2 + a i3 X 3 + ...... + a in X n + F i
..................................................................
..................................................................
X n = a n1 X 1 + a n2 X 2 + a n3 X 3 + ...... + a nn X n + F n
;kofDe d/ o{g ftZu fbyD s/

or X = AX + F ....(I)
fJj nkrs^fBors wkvb dk ;XkoD ;wheoD j[zdh j?.

26H2 pzd nkrs^fBors w'vb (Closed Input-Output Model)
i/eo pkjoh y/so dh wzr Gkt F, nzdo{Bh y/so dh soQK ekoi eo/ sK T[j w'vb pzd nkdk^gqdk
j?. fi; soQK nkyoh T[gG'r y/so, j'o T[d:'rK B{z wId{oK dh g{osh eodk j? sK T[j fJZe

340 LOVELY PROFESSIONAL UNIVERSITY