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