If A = [5-34-3-21], Prove that (2A)T = 2AT - Mathematics and Statistics

Question

If A = `[(5, -3),(4, -3),(-2, 1)]`, Prove that (2A)^T = 2A^T

Sum

Solution

A = `[(5, -3),(4, -3),(-2, 1)]`

∴ 2A = `2[(5, -3),(4, -3),(-2, 1)] = [(10, -6),(8, -6),(-4, 2)]`

∴ (2A)^T = `[(10, 8, -4),(-6, -6, 2)]` ...(i)

A^T = `[(5, 4, -2),(-3, -3, 1)]`

∴ 2A^T = `[(5, 4, -2),(-3, -3, 1)]`

= `[(10, 8, -4),(-6, -6, 2)]` ...(ii)

From (i) and (ii), we get

(2A)^T = 2A^T

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

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Balbharati Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board

Chapter 4 Determinants and Matrices
Exercise 4.7 | Q 3 | Page 97

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