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Question
Answer the following question:
If A = `[(2, -3),(3, -2),(-1, 4)]`, B = `[(-3, 4, 1),(2, -1, -3)]` Verify (A + 2BT)T = AT + 2B
Solution
A = `[(2, -3),(3, -2),(-1, 4)]` and B = `[(-3, 4, 1),(2, -1, -3)]`
∴ AT = `[(2, 3, -1),(-3, -2, 4)]` and BT = `[(-3, 2),(4, -1),(1, -3)]`
∴ A + 2BT = `[(2, -3),(3, -2),(-1, 4)] + 2 [(-3, 2),(4, -1),(1, -3)]`
= `[(2, -3),(3, -2),(-1, 4)] + [(-6, 4),(8, -2),(2, -6)]`
∴ A + 2BT = `[(-4, 1),(11, -4),(1, -2)]`
∴ (A + 2BT)T = `[(-4, 11, 1),(1, -4, -2)]` ...(i)
AT + 2B = `[(2, 3, -1),(-3, -2, 4)] + 2[(-3, 4, 1),(2, -1, -3)]`
= `[(2, 3, -1),(-3, -2, 4)] + [(-6, 8, 2),(4, -2, -6)]`
= `[(-4, 11, 1),(1, -4, -2)]` ...(ii)
From (i) and (ii), we get
(A + 2BT)T = AT + 2B
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