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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).
Solution
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)
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