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

fJekJh^21 L ;kofDe L gqeko ns/ r[D^Xow

21H1 ;kofDe dh gfoGkPk (Definition of Determinant) B'N

fBwBfbys d' fJZexksh ;wheoDK T[Zs/ ftuko eo'^
a 1 x + b 1 y = 0 ....(i)

a 2 x + b 2 y = 0 ....(ii)
T[go'es ;wheoDK d[nkok x ns/ y dk ftbhnB (Elimination) eoB d/ bJh ;wheoD (i) B{z a 2
d[nkok ns/ ;wheoD (ii) B{z a 1 eoe/ xNkT[D s/
(b 1 a 2 – b 2 a 1 ) y = 0

iK b 1 a 2 – b 2 a 1 = 0
iK a 1 b 2 – a 2 b 1 = 0
ftnzie (a 1 b 2 – a 2 b 1 ) B{z fBwB fbys o{g ftZu gqdofPs ehsk frnk j?^

fi;B{z ;kofDe (Determinant) efjzd/ jB.

∴

ftnzie (a 1 b 2 – a 2 b 1 ) B{z fJ; ;kofDe dk gq;ko (Expansion) iK wkB (Value) efjzd/ jB.
T[go'es ;kofDe ftZu d' gzeshnK (Rows) ns/ d' ;szG (Columns) jB. fJ; bJh T[go'es
;kofDe, d{ih e'Nh iK d{i/ eqw (Second Order) dk ;kofDe ejkT[Adk j?. ftnzie (a 1 b 2 – a 2 b 1 )
B{z fJ; ;kofDe dk ft;Eko (Expansion) efjzd/ jB. a 1 , a 2 , b 1 , b 2 ;kofDe d/ ;zxNe
(Constituents) ejkT[Ad/ jB ns/ a 1 , b 2 ns/ a 2 , b 1 fJ;d/ nzr (Elements) ejkT[Ad/ jB.
j[D fBwBfbys fszB fJZexksh ;wheoDK T[Zs/ ftuko eo'^
a 1 + b 1 y + c 1 z = 0
a 2 + b 2 y + c 2 z = 0
a 3 + b 3 y + c 3 z = 0
fJBQK fszB'A ;wheoDK d[nkok x, y, z dk ftb'gB eoB s/ fBwBfbys cb gqkgs j[zdk j?^
a 1 (b 2 c 3 – b 3 c 2 ) – b 1 (a 2 c 3 – a 3 c 2 ) + c 1 (a 2 b 3 – a 3 b 2 ) = 0
iK
a 1 (b 2 c 3 – b 3 c 2 ) – a 2 (b 1 c 3 – b 3 c 1 ) + a 3 (b 1 c 2 – b 2 c 1 ) = 0
gqkgs cb ftZu gqkgs yZp/ gk;/ d/ ftnzie B{z fBwB fbys o{g ftZu gqdofPs ehsk frnk j?^

fi;B{z fsZih e'Nh (Third Order) dk ;kofDe efjzd/ jB. fsZih e'Nh d/ ;kofDe ftZu fszB
gzeshnK (Rows) ns/ fszB ;szG (Columns) j[zd/ jB.

B'N; yZp/ gk;/ d/ ftnzie B{z T[go'es ;kofDe dk gq;ko (Expansion) iK wkB (Value)
efjzd/ jB.

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