Question

If A^T = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following 

(A – B)^T = A^T – B^T

Answer 1

A^T = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`

A – B = `[(4, - 1, 2),(5, 0, 3)] - [(2, -1, 1),(7, 5, -2)]`

= `[(4 - 2, -1 + 1, 2 - 1),(5 - 7, 0 - 5, 3 + 2)]`

A – B = `[(2, 0, 1),(-2, -5, -5)]`

(A – B)^T = `[(2, 2),(0, -5),(1, 5)]`  .......(4)

A^T – B^T = `[(4, 5),(-1, 0),(2, 3)] - [(2, 7),(-1, 5),(1, -2)]`

= `[(4 - 2, 5 -7),(-1 + 1, 0 - 5),(2 - 1, 3 + 2)]`

A^T – B^T = `[(2, 2),(0, -5),(1, 5)]`   ......(5)

From equation (1) and (2)

(A – B)^T = A^T – B^T