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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

noEPk;soh dk rfDs

B'N 21H7 d' ;kofDeK dk r[DBcb (Multiplication of Two Determinants)

d' ;kofDeK dk r[DBcb e/tb T[;h dPk ftZu gsk ehsk ik ;edk j? id'A T[j d'B'A ;wkB e'Nh
(Same Order) d/ j'D, BjhA sK BjhA.
y
a c x z
b
1 1 1 1 1 1
wzfBnk A = a c ns/ B = x z
b
y
2 2 2 2 2 2
y
a 3 c 3 x 3 z 3
b
3
3
fsZih e'Nh (Third Order) d/ d' ;kofDe jB. fJBQK dk r[DBcb, fijVk AB d[nko ftnes
ehsk iKdk j?, fJZe fsZih e'Nh dk jh ;kofDe j't/rk fi;B{z j/m nB[;ko gsk eod/ jB^
gfjbK ;kofDe A dh gfjbh gzesh (a 1 b 1 c 1 ) B{z ;fEo oZy e/ fJ;d/ ;zxNeK dh, d{i/ ;kofDe B
dh gfjbh, d{ih ns/ fsZih gzesh d/ ;zrs ;zxNeK s'A tZy^tZy r[Dk eo' ns/ T[jBK d/ tZy^tZy
:'rcb gsk eo' fit/A j/mK fdykfJnk frnk j?^

i'V &

T[go'es fszB'A i'Vcb ;kofDe AB dh gfjbh gzesh d/ eqw nB[;ko gfjb/, d{i/, fsZi/ ;zxNe
j'Dr/.
fJ;h soQK, ;kofDe A dh d{ih gzesh (a 2 b 2 c 2 ) B{z ;fEo oZye/, d{i/ ;kofDe B dhnK fszB'A
gzeshnK d/ ;zrs ;zxNeK Bkb r[Dk eoe/ tZy^tZy :'rcb gsk eo' fijV/ ;kofDe AB dhnK
d{ihnK gzeshnK d/ ;zxNe j'Dr/.
fJjh fefonk A dh fsZih gzesh (a 3 b 3 c 3 ) ns/ B dhnK ;kohnK gzeshnK d/ Bkb ehsh iKdh j?.
fJ; soQK A ns/ B dk r[DBcb & AB

jZb eoB dh ftXh (Working Rule)
T[Zgo fdZs/ rJ/ r[DK dh ;jkfJsk Bkb fe;h th gzesh iK fJZe ;szG ftZu ;zGt sohe/ Bkb
‘Iho'’ pDkU ns/ ;kofDe dk ft;Eko T[;h gzeshf iK ;szG d/ ;zxNeK d/ ;kg/y eo'.
gqPBK d/ jZb ftZu gfjbh, d{ih, fsZih,HHHHHHHnkfd gzeshnK (Rows) B{z eqw nB[;ko R 1 , R 2 , R 3 ,
......nkfd Bkb ns/ gfjb/, d{i/, fsZi/,HHHHHHH, nkfd ;szGK (Columns) B{z eqw nB[;ko C 1 , C 2 ,
C 3 ,......nkfd Bkb do;kT[Ad/ jB ns/ ;kofDe dhnK gzeshnK ns/ ;szGK d/ ftZu i' th fefonk
eod/ jB. T[;B{z ;kofDe d/ ;Zi/ gk;/ fby fdzd/ jB.
T[dkjkoD 1H fBwBfbys ;kofDe dk wkB gsk eo'^

13 16 19
14 17 20 = 0 H
14 18 21

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