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Question
If A = `[(1, 2),(4, 1),(5, 6)]` B = `[(1, 2),(6, 4),(7, 3)]`, then verify that: (2A + B)′ = 2A′ + B′
Solution
Given that: A = `[(1, 2),(4, 1),(5, 6)]` and B = `[(1, 2),(6, 4),(7, 3)]`
L.H.S. (2A + B)' = `[2((1, 2),(4, 1),(5, 6)) + ((1, 2),(6, 4),(7, 3))]^'`
= `[((2, 4),(8, 2),(10, 12)) + ((1, 2),(6, 4),(7, 3))]^'`
= `[(2 + 1, 4 + 2),(8 + 6, 2 + 4),(10 + 7, 12 + 3)]^'`
= `[(3, 6),(14, 6),(17, 15)]^'`
= `[(3, 14, 17),(6, 6, 15)]`
R.H.S. 2A' + B' = `2[(1, 2),(4, 1),(5, 6)]^' + [(1, 2),(6, 4),(7, 3)]^'`
= `2[(1, 4, 5),(2, 1, 6)] + [(1, 6, 7),(2, 4, 3)]`
= `[(2, 8, 10),(4, 2, 12)] + [(1, 6, 7),(2, 4, 3)]`
= `[(2 + 1, 8 + 6, 10 + 7),(4 + 2, 2 + 4, 12 + 3)]`
= `[(3, 14, 17),(6, 6, 15)]`
Hence, L.H.S. = R.H.S.
(2A + B)′ = 2A′ + B′ is verified.
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