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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 + b)B = aB + bB
Solution
We have,
A = `[(1, 2),(-1, 3)]`
B = `[(4, 0),(1, 5)]`
C = `[(2, 0),(1, -2)]`
And a = 4, b = –2
(a + b)B = `(4 - 2) [(4, 0),(1, 5)]` .....[∵ Given a = 4, b = –2]
= `[(8, 0),(2, 10)]`
Also, aB + bB
= 4B – 2B
= `[(16, 0),(4, 20)] - [(8, 0),(2, 10)]`
= `[(8, 0),(2, 10)]`
= `(a + b)B
Hence proved.
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