If and verify that A(B – C) = (AB – AC).

Question

If  and  verify that A(B – C) = (AB – AC).

Philoid · Accepted Answer

Given : and

Matrix A is of order 3 3; matrix B is of order 3 3 and matrix C is of order 3 3

To verify : A(B – C) = (AB – AC).

The formula used :

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 = 3,thus matrix A(B + C) is of order 3 x 3

A(B - C) =

A(B - C) = =

A(B - C) =

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

Matrix AB =

Matrix AB = =

Matrix AB =

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

Matrix AC =

Matrix AC = =

Matrix AC =

Matrix AB - AC = =

Matrix AB - AC =

A(B – C) = (AB – AC) =