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