Question

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

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)C = `[(-3, 2),(0, -2)] xx [(2, 0),(1, 2)]`

= `[(-6 + 2, 0 + 4),(0 - 2, 0 - 4)]`

= `[(-4, 4),(-2, -4)]`  ...(1)

AC = `[(1, 2),(1, 3)] xx [(2, 0),(1, 2)]`

= `[(2 + 2, 0 + 4),(2 + 3, 0 + 6)]`

= `[(4, 4),(5, 6)]`

BC = `[(4, 0),(1, 5)] xx [(2, 0),(1, 2)]`

= `[(8 + 0, 0 + 0),(2 + 5, 0 + 10)]`

= `[(8, 0),(7, 10)]`

AC – BC = `[(4, 4),(5, 6)] - [(8, 0),(7, 10)]`

= `[(-4, 4),(-2, -4)]`  ...(2)

From (1) and (2) we get

(A – B)C = AC – BC