Question

If A = `[(1, 2),(4, 1),(5, 6)]` B = `[(1, 2),(6, 4),(7, 3)]`, then verify that: (A – B)′ = A′ – B′

Answer 1

Given that: A = `[(1, 2),(4, 1),(5, 6)]` and B = `[(1, 2),(6, 4),(7, 3)]`

L.H.S. (A – B)' = `[((1, 2),(4, 1),(5, 6)) - ((1, 2),(6, 4),(7, 3))]^'`

= `[(1 - 1, 2 - 2),(4 - 6, 1 - 4),(5 - 7, 6 - 3)]^'`

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

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

R.H.S. A' – B' = `[(1, 2),(4, 1),(5, 6)]^' - [(1, 2),(6, 4),(7, 3)]^'`

= `[(1, 4, 5),(2, 1, 6)] -[(1, 6, 7),(2, 4, 3)]`

= `[(1 - 1, 4 - 6, 5 - 7),(2 - 2, 1 - 4, 6 - 3)]`

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

Hence, L.H.S. = R.H.S.

(A – B)′ = A′ – B′ is verified.