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Question
Find x and y, if `[(2x + y, -1, 1),(3, 4y, 4)] [(-1, 6, 4),(3, 0, 3)] = [(3, 5, 5),(6, 18, 7)]`.
Solution
`[(2x + y, -1, 1),(3, 4y, 4)] [(-1, 6, 4),(3, 0, 3)] = [(3, 5, 5),(6, 18, 7)]`
∴ `[(2x + y - 1, -1 + 6, 1 + 4),(3 + 3, 4y + 0, 4 + 3)] = [(3, 5, 5),(6, 18, 7)]`
∴ `[(2x + y - 1, 5, 5),(6, 4y, 7)] = [(3, 5, 5),(6, 18, 7)]`
∴ By equality of matrices, we get
2x + y – 1 = 3 and 4y = 18
∴ 2x + y = 4 and y = `(18)/(4) = (9)/(2)`
∴ `2x + 9/2` = 4
∴ 2x = `4 - (9)/(2)`
∴ 2x = `- (1)/(2)`
∴ x = `-(1)/(4)` and y = `(9)/(2)`
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