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