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Question
Find x and y, if `[(3, -2),(-1, 4)][(2x),(1)] + 2[(-4),(5)] = 4[(2),(y)]`
Solution
Given:
`[(3,-2),(-1,4)][(2x),(1)] + 2[(-4),(5)] = 4[(2),(y)]`
`[(3 xx 2x + (-2)(1)),(-1 xx 2x + 4(1))] + [(-8),(10)] = [(8),(4y)]`
`[(6x - 2),(-2x + 4)] + [(-8),(10)] = [(8),(4y)]`
`[(6x - 2 - 8),(-2x + 4 x + 10)] = [(8),(4y)]`
`[(6x - 10),(-2x + 14)] = [(8), (4y)]`
Now, comparing the corresponding elements of two equal matrices; we have
6x – 10 = 8
∴ 6x = 18
∴ x = `(18)/(6)` = 3 ...(Using x = 3)
And 4y = –2x + 14
4y = –2 × 3 + 14
`\implies` 4y = 14 – 6 = 8
i.e. y = `(8)/(4)` = 2
Thus, `{{:(x = 3),(y = 2):}}`
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