Find x and y, if {4[2-13102]-[3-34211]}[2-11]=[xy] - Mathematics and Statistics

Question

Find x and y, if `{4[(2, -1, 3),(1, 0, 2)] -[(3, -3, 4),(2, 1, 1)]} [(2),(-1),(1)] = [(x),(y)]`

Sum

Solution

`{4[(2, -1, 3),(1, 0, 2)] -[(3, -3, 4),(2, 1, 1)]} [(2),(-1),(1)] = [(x),(y)]`

∴ `{[(8, -4, 12),(4, 0, 8)] -[(3, -3, 4),(2, 1, 1)]} [(2),(-1),(1)] = [(x),(y)]`

∴ `[(8 - 3, -4 + 3, 12 - 4),(4 - 2, 0 - 1, 8 - 1)] [(2),(-1),(1)] = [(x),(y)]`

∴ `[(5, -1, 8),(2, -1, 7)] [(2),(-1),(1)] = [(x),(y)]`

∴ `[(10 + 1 + 8),(4 + 1 + 7)] = [(x), (y)]`

∴ `[(19),(12)] = [(x),(y)]`

∴ By equality of matrices, we get

x = 19 and y = 12

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Chapter 4: Determinants and Matrices - Exercise 4.6 [Page 95]

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

Chapter 4 Determinants and Matrices
Exercise 4.6 | Q 21 | Page 95

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