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Question
If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (kA)' = (kA')
Solution
Given that: A = `[(0, -1, 2),(4, 3, -4)]`, B = `[(4, 0),(1, 3),(2, 6)]`
L.H.S. kA = `"k"[(0, -1, 2),(4, 3, -4)]`
= `[(0, -"k", 2"k"),(4"k", 3"k", -4"k")]`
(kA)' = `[(0, 4"k"),(-"k", 3"k"),(2"k", -"k")]`
R.H.S. kA' = `"k"[(0, -1, 2),(4, 3, -4)]^'`
= `"k"[(0, 4),(-1, 3),(2, -4)]`
= `[(0, 4"k"),(-"k", 3"k"),(2"k", -4"k")]`
Hence, L.H.S. = R.H.S.
(kA)' = (kA') is verified.
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