Question

If A = `[(2, 1)]`, B = `[(5, 3, 4),(8, 7, 6)]` and C = `[(-1, 2, 1),(1, 0, 2)]`, verify that A(B + C) = (AB + AC).

Answer 1

We have A = `[(2, 1)]`, B = `[(5, 3, 4),(8, 7, 6)]` and C = `[(-1, 2, 1),(1, 0, 2)]`

∴ A(B + C) = `[(2, 1)] [(5 - 1, 3 + 2, 4 + 1),(8 + 1, 7 + 0, 6 + 2)]`

= `[(2, 1)] [(4, 5, 5),(9, 7, 8)]`

= `[(8 + 9, 10 + 7, 10 + 8)]`

= `[(17, 17, 18)]`  ......(i)

Now AB = `[(2, 1)] [(5, 3, 4),(8, 7, 6)]`

= `[(10 + 8, 6 + 7, 8 + 6)]`

= `[(18, 3, 14)]`

And AC =`[(2, 1)] [(-1, 2, 1),(1, 0, 2)]`

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

 `[(-1, 4, 4)]`

∴ AB + AC = `[(18, 13, 14)] + [(-1, 4, 4)]`

= `[(17, 17, 18)]`  ......(ii)

From equations (i) and (ii)

 A(B + C) = (AB + AC)