Question

If A = `[(1, 2),(3, 4)], B = [(6, 1),(1, 1)]` and C = `[(-2, -3),(0, 1)]`, find each of the following and state if they are equal:

1. CA + В
2. A + СВ

Answer 1

(i)

CA + B

CA = `[(-2, -3),(0, 1)] xx [(1, 2),(3, 4)]`

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

= `[(-2 - 9, -4 - 12),(3, 4)]`

= `[(-11, -16),(3, 4)]`

CA + B = `[(-11, -16),(3, 4)] + [(6, 1),(1, 1)]`

= `[(-11 + 6, -16 + 1),(3 + 1, 4 + 1)]`

= `[(-5, -15),(4, 5)]`

(ii)

A + CB

CB = `[(-2, -3),(0, 1)] xx [(6, 1),(1, 1)]`

= `[(-2 xx 6 + (-3) xx 1, -2 xx 1 + (-3) xx 1),(0 xx 6 + 1 xx 1, 0 xx 1 + 1 xx 1)]`

= `[(-12 - 3, -2 -3),(1, 1)]`

= `[(-15, -5),(1, 1)]`

A + CB = `[(1, 2),(3, 4)] + [(-15, -5),(1, 1)]`

= `[(1 + (-15), 2 + (-5)),(3 + 1, 4 + 1)]`

= `[(-14, -3),(4, 5)]`

CA + B = `[(-5, -15),(4, 5)]`

A + CB = [(-14, -3),(4, 5)]`

CA + B ≠ A + CB