If A = [2-13-241] and B = [03-42-11], verify that (AB)T = BT AT - Mathematics and Statistics

Question

If A = `[(2, -1),(3, -2),(4, 1)]` and B = `[(0, 3, -4),(2, -1, 1)]`, verify that (AB)^T = B^T A^T

Sum

Solution

AB = `[(2, -1),(3, -2),(4, 1)] [(0, 3, -4),(2, -1, 1)]`

= `[(0 - 2, 6 + 1, -8 - 1),(0 - 4, 9 + 2, -12 - 2),(0 + 2, 12 - 1, -16 + 1)]`

= `[(-2, 7, -9),(-4, 11, -14),(2, 11, -15)]`

∴ (AB)^T = `[(-2, -4, 2),(7, 11, 11),(-9, -14, -15)]` ...(1)

A^T = `[(2, 3, 4),(-1, -2, 1)]` and B^T = `[(0, 2),(3, -1),(-4, 1)]`

∴ B^TA^T = `[(0, 2),(3, -1),(-4, 1)] [(2, 3, 4),(-1, -2, 1)]`

= `[(0 - 2, 0 - 4, 0 + 2),(6 + 1, 9 + 2, 12 - 1),(-8 - 1, -12 - 2, -16 + 1)]`

= `[(-2, -4, 2),(7, 11, 11),(-9, -14, -15)]` ...(2)

From (1) and (2),

(AB)^T = B^TA^T

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Q 13. (i)Q 12. (ii)Q 13. (ii)

Chapter 4: Determinants and Matrices - Exercise 4.7 [Page 98]

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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 13. (i) | Page 98

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