Q. 7 A5.0( 3 Votes )

Verify that A(B + C) = (AB + AC), when

and

Answer :

Given : and


Matrix A is of order 2 2 , matrix B is of order 2 2 and matrix C is of order 2 2


To verify : A(B + C) = (AB + AC)


Formula used :



Where cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj


If A is a matrix of order a b and B is a matrix of order c d ,then matrix AB exists and is of order a d ,if and only if b = c


If A is a matrix of order a b and B is a matrix of order c d ,then matrix BA exists and is of order c b ,if and only if d = a


B + C = + = =


B + C =


Matrix A(B + C) is of order 2 x 2


A(B + C) = =


A(B + C) = =


A(B + C) =


For matrix AB, a = b = c = d = 2 ,matrix AB is of order 2 x 2


Matrix AB = =


Matrix AB = =


Matrix AB =


For matrix AC, a = b = c = d = 2 ,matrix AC is of order 2 x 2


Matrix AC = =


Matrix AC = =


Matrix AC =


Matrix AB + AC = + = =


Matrix AB + AC = A(B + C) =


A(B + C) = (AB + AC)


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