Question

Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that (A – B)^T = A^T – B^T

Answer 1

A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]`

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

= `[(-3, 2),(0, 2)]`

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

A^T = `[(1, 1),(2, 3)]`

B^T = `[(4, 1),(0, 5)]`

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

= `[(-3, 0),(2, -2)]` ...(2)

From (1) and (2) we get

(A – B)^T = A^T – B^T