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If A = [12-52-34-549], Prove that (3A)T = 3AT - Mathematics and Statistics

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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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Chapter 4: Determinants and Matrices - Exercise 4.7 [Page 97]

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