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Question
If matrix A = `[(x - y, x + y),(y - x, y + x)]` and matrix B = `[(x + y, y - x),(x - y, y + x)]` then A + B is ______.
Options
`[(2y, 2),(0, 2(x + y))]`
`[(2x, 2(x + y)),(0, 0)]`
`[(2x, 2y),(0, 2(x + y))]`
`[(2x - 2y, 2y),(0, 0)]`
Solution
If matrix A = `[(x - y, x + y),(y - x, y + x)]` and matrix B = `[(x + y, y - x),(x - y, y + x)]` then A + B is `underlinebb([(2x, 2y),(0, 2(x + y))])`.
Explanation:
A + B = `[(x - y, x + y),(y - x, y + x)] + [(x + y, y - x),(x - y, y + x)]`
= `[(x - y + x + y, x + y + y - x),(y - x + x - y, y + x + y + x)]`
= `[(2x, 2y),(0, 2(x + y))]`
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