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Question
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: a(C – A) = aC – aA
Solution
We have,
A = `[(1, 2),(-1, 3)]`
B = `[(4, 0),(1, 5)]`
C = `[(2, 0),(1, -2)]`
And a = 4, b = –2
C – A = `[(, ),(1, -2)] - [(1, 2),(-1, 3)]`
= `[(1, -2),(2, -5)]`
And a(C – A) = 4(C – A)
= `[(4, -8),(8, -20)]`
Also, aC – aA = 4C – 4A
= `[(8, 0),(4, -8)] - [(4, 8),(-4,12)]`
= `[(4, -8),(8, -20)]`
= a(C – A)
Hence proved
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