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Question
Answer the following question:
Find x, y if, `{-1 [(1, 2, 1),(2, 0, 3)] + 3[(2, -3, 7),(1, -1, 3)]} [(5),(0),(-1)] = [(x),(y)]`
Solution
`{-1 [(1, 2, 1),(2, 0, 3)] + 3[(2, -3, 7),(1, -1, 3)]} [(5),(0),(-1)] = [(x),(y)]`
∴ `{[(-1, -2, -1),(-2, 0, -3)] + [(6, -9, 21),(3, -3, 9)]} [(5),(0),(-1)] = [(x),(y)]`
∴ `[(5, -11, 20),(1, -3, 6)] [(5),(0),(-1)] = [(x),(y)]`
∴ `[(25 - 0 - 20),(5 - 0 - 6)] = [(x),(y)]`
∴ `[(5),(-1)] = [(x),(y)]`
∴ By equality of matrices, we get
x = 5, y = – 1
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