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

and

Given : and

Matrix A is of order 3 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 c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

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 =

For Matrix A(B + C), a = 3,b = c = d = 2,thus matrix A(B + C) is of order 3 x 2

A(B + C) = =

A(B + C) = =

A(B + C) =

For matrix AB, a = 3, b = c = d = 2 ,matrix AB is of order 3 x 2

Matrix AB = =

Matrix AB = =

Matrix AB =

For matrix AC, a = 3, b = c = d = 2 ,matrix AC is of order 3 x 2

Matrix AC = =

Matrix AC = =

Matrix AC =

Matrix AB + AC = + = =

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

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