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Question
Find x, y if `[(-2, 0),(3, 1)] [(-1),(2x)] +3[(-2),(1)] = 2[(y),(3)]`.
Solution 1
`[(-2, 0),(3, 1)] [(-1),(2x)] +3[(-2),(1)] = 2[(y),(3)]`
`[(2 +0),(-3 + 2x)] + [(-6),(3)] = [(2y),(6)]`
`[(-4),(2x)] = [(2y),(6)]`
⇒ 2y = -4, 2x = 6
⇒ y = -2, x = 3
Thus required values is x = 3, y = -2.
Solution 2
Given
`[(-2, 0),(3, 1)] [(-1),(2x)] +3[(-2),(1)] = 2[(y),(3)]`
`[(-2x - 1 + 0 xx 2x),(3x - 1 + 1 xx 2x)] + [(-6),(3)] = [(2y),(6)]`
`[(2 +0),(-3 + 2x)] + [(-6),(3)] = [(2y),(6)]`
`[(2 - 6),(-3 + 2x + 3)] = [(2y),(6)]`
⇒ `[(-4),(2x)] = [(2y),(6)]`
⇒ 2x = 6 and 2y = –4
⇒ x = `(6)/(2)` and y = `-(4)/(2)`
⇒ x = 3 and ⇒ y = –2.
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