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Question
Find x, y, z if `{3[(2, 0),(0, 2),(2, 2)] -4[(1, 1),(-1, 2),(3, 1)]} [(1),(2)]` = `[("x" - 3),("y" - 1),(2"z")]`
Solution
`{3[(2, 0),(0, 2),(2, 2)] -4[(1, 1),(-1, 2),(3, 1)]} [(1),(2)] = [("x" - 3),("y" - 1),(2"z")]`
∴ `{[(6, 0),(0, 6),(6, 6)] - [(4, 4),(-4, 8),(12, 4)]} [(1),(2)] = [("x" - 3),("y" - 1), (2"z")]`
∴ `[(6 - 4, 0-4),(0+4, 6-8),(6-12, 6-4)] [(1),(2)] = [("x" - 3),("y" - 1), (2"z")]`
∴ `[(2, -4),(4, -2),(-6, 2)] [(1),(2)] = [("x" - 3),("y" - 1), (2"z")]`
∴ `[(2 - 8),(4 - 4),(-6 + 4)] = [("x" - 3),("y" - 1),(2"z")]`
∴ `[(-6),(0),(-2)] = [("x" - 3),("y" - 1),(2"z")]`
∴ by equality of matrices,
x – 3 = –6, y – 1 = 0, 2z = – 2
∴ x = – 3, y = 1, z = –1.
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