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Question
Answer the following question:
Find x, y, z if `{5[(0, 1),(1, 0),(1, 1)] -3[(2, 1),(3, -2),(1, 3)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`
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Solution
`{5[(0, 1),(1, 0),(1, 1)] -3[(2, 1),(3, -2),(1, 3)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`
∴ `{[(0, 5),(5, 0),(5, 5)] - [(6, 3),(9, -6),(3, 9)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`
∴ `[(-6, 2),(-4, 6),(2, -4)] [(2),(1)] = [(x - 1),(y + 1),(2z)]`
∴ `[(-12 + 2),(-8 + 6),(4 - 4)] = [(x - 1),(y + 1),(2z)]`
∴ `[(-10),(-2),(0)] = [(x - 1),(y + 1),(2z)]`
∴ By equality of matrices, we get
x – 1 = – 10
∴ x = – 9
y + 1 = – 2
∴ y = – 3
2z = 0
∴ z = 0
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