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Question
If A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`, Prove that (3A)T = 3AT
Sum
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Solution
A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
∴ AT = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
∴ 3AT = `3[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
= `[(3, 6, -15),(6, -9, 12),(-15, 12, 27)]` ...(1)
3A = `3[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
= `[(3, 6, -15),(6, -9, 12),(-15, 12, 27)]`
∴ (3A)T = `[(3, 6, -15),(6, -9, 12),(-15, 12, 27)]` ...(2)
From (1) and (2),
(3A)T = 3AT.
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