Page 332 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math21-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12 VIIth 11-5-13

vFkZ'kkfL=k;ksa dk xf.kr

uksV ;fn lkjf.kd dh fdlh ,d gh iafDr vFkok LrEHk dks fdlh jkf'k ls xq.kk djrs gSa rks iwjs
lkjf.kd dks ml jkf'k ls Hkkx dj nsuk pkfg,A

mnkgj.kkFkZµ
a 1 b 1 c 1 ka 1 kb 1 kc 1
a 2 b 2 c 2 4 1 a 2 b 2 c 2
a 3 b 3 c 3 k a 3 b 3 c 3

5- ;fn lkjf.kd esa fdlh iafDr vFkok LrEHk dk izR;sd vo;o nks jkf'k;ksa dk ;ksxiQy gks rks ml lkjf.kd
dks mlh dksfV osQ nks lkjf.kdksa osQ ;ksxiQy osQ :i esa iznf'kZr fd;k tk ldrk gSA

mnkgj.kkFkZµ
a + p b 1 c 1 a 1 b 1 c 1 p b 1 c 1
1
a + q b 2 c 2 4 a 2 b 2 c 2 3 q b 2 c 2
2
a + r b 3 c 3 a 3 b 3 c 3 r b 3 c 3
3
6- ;fn lkjf.kd dh fdlh iafDr vFkok LrEHk dks lHkh vo;oksa dks fdlh fuf'pr jkf'k ls xq.kk djosQ
fdlh vU; iafDr vFkok LrEHk osQ laxr vo;oksa esa tksM+ vFkok ?kVk fn;k tk;s rks lkjf.kd dk eku
vifjofrZr jgrk gSA
mnkgj.kkFkZµ∆′ 4 ∆, tcfd
a + 1 mb − 1 nc 1 b 1 c 1 a 1 b 1 c 1
a + 2 mb − 2 nc 2 b 2 c 2 ∆ = a 2 b 2 c 2
a + 3 mb − 3 nc 3 b 3 c 3 a 3 b 3 c 3

lkjf.kd osQ iz'uksa dks gy djus esa bl xq.k dk fo'ks"k egÙo gSA bl xq.k osQ vuqlkj lkjf.kd esa] fdlh iafDr
osQ vo;oksa esa fdlh vU; iafDr vFkok iafDr;ksa osQ laxr vo;oksa dk fdrus gh xquk tksM+k vFkok ?kVk;k tk
ldrk gSA ;gh fØ;k LrEHkksa esa Hkh dh tk ldrh gSA

21-7 nks lkjf.kdksa dk xq.kuiQy !
"

nks lkjf.kdksa dk xq.kuiQy osQoy mlh n'kk esa Kkr fd;k tk ldrk gS tc os nksuksa leku dksfV
osQ gksa] vU;Fkk ughaA
a 1 b 1 c 1 x 1 y 1 z 1
ekuk 4 a 2 b 2 c 2 B = x 2 y 2 z 2
a 3 b 3 c 3 x 3 y 3 z 3

r`rh; dksfV * osQ nks lkjf.kd gSaA budk xq.kuiQy] tks
ls O;Dr fd;k tkrk gS] ,d r`rh;
dksfV dk gh lkjf.kd gksxk ftls fuEu izdkj Kkr djrs gSaµ
igys lkjf.kd dh igyh iafDr dks fLFkj j[kdj blosQ vo;oksa dh] nwljs lkjf.kd
dh igyh]

nwljh rFkk rhljh iafDr osQ laxr vo;oksa ls vyx&vyx xq.kk djks vkSj muosQ vyx&vyx ;ksxiQy Kkr djks
tSlk uhps fn[kk;k x;k gSµ