If A = [2-35-4-61], B = [214-1-33] and C = [12-14-23] then show that (A + B) = AT + BT - Mathematics and Statistics

Question

If A = `[(2, -3),(5, -4),(-6, 1)]`, B = `[(2, 1),(4, -1),(-3, 3)]` and C = `[(1, 2),(-1, 4),(-2, 3)]` then show that (A + B)^T = A^T + B^T

Sum

Solution

A + B = `[(2, -3),(5, -4),(-6, 1)] +[(2, 1),(4, -1),(-3, 3)]`

= `[(2 + 2, -3 + 1),(5 + 4, -4 - 1),(-6 - 3, 1 + 3)]`

= `[(4, -2),(9, -5),(-9, 4)]`

∴ (A + B)^T = `[(4, 9, -9),(-2, -5, 4)]` ...(i)

Now, A^T = `[(2, 5, -6),(-3, -4, 1)]` and B^T = `[(2, 4, -3),(1, -1, 3)]`

∴ A^T + B^T = `[(2, 5, -6),(-3, -4, 1)] + [(2, 4, -3),(1, -1, 3)]`

= `[(2 + 2, 5 + 4, -6 - 3),(-3 + 1, -4 - 1, 1 + 3)]`

= `[(4, 9, -9),(-2, -5, 4)]` ...(ii)

From (i) and (ii), we get

(A + B)^T = A^T + B^T

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Matrices - Properties of Transpose of a Matrix

Is there an error in this question or solution?

Q 6. (i)Q 5 Q 6. (ii)

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 6. (i) | Page 97

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