Page 281 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

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E L-LOVELY-H math18-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^18 L t:{j (w?fNqe;) L noE ns/ gqeko

0 1  1 0  B'N
T[dkjoD 4H i/eo A =   ns/ B =  
 0 0   0 0 
j't/, sK AB dk wkB eZY'.
 01   1 0   0 0

jZb L A =     =   = 0

 00   00   00 
fJ; s'A fJj f;ZX j[zdk j? fe w?fNqe; r[DB fJZe Iho' w?fNqe; j? gozs{ A ≠ 0 ns/ B ≠ 0
t:{j r[DB dk ;fjuo fB:w
(i) w?fNqe; r[DB dk ;fjuo fB:w (Associative Law of Matrix Multiplication)
i/eo A = [a ij ] m × n eqw dk j?, B = [b ik ], n × p eqw dk j? ns/ C = [c ik ], p × q eqw dk j?, T[d'A
A (B . C) = (A . B) . C, d'B'A gZy m × q eqw d/ w?fNqe; jB, Gkt w?fNqe; r[DB ;fjukoh jB.
fJj ;obsk Bkb f;ZX eo ;ed/ jK.

wzB fbU fiZE/ B. C = [d ji ], fiZE/

fJ; soQK A . (B . C) = [c ij ], fiZE/ c ji = a i1 d 1i + .....a in d ni

feT[Ai' gdK dh ;zfynk gfofws j?, fJ; bJh :'r dk eqw gfotosB s/

(ii) w?fNqe; r[DB dh tzv fB:w (Distributive Law of Matrix Multiplication)
i/eo A = [a ij ], m × n eqw dk j?, ns/ B = [b ik ], C = [c jk ], n × p eqw d/ jB,
T[d'A

feT[Ai'
fJ; soQK
fiZE/

fJ; soQK
fJ; soQK A (B + C) = AB + AC
fJ;h soQK i/eo B = [b ik ], C = [c jk ], n × p eqw d/ jB ns/ A = [a ij ], p × n eqw dk j?, T[d'A (B + C)
A = BA + CA.

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