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Question
Find matrices X and Y, if X + Y =`[[5 2],[0 9]]`
and X − Y = `[[3 6],[0 -1]]`
Solution
Given: `(X+Y)+(X-Y)=[[5 2],[0 9]]+` `[[3 6],[0 -1]]`
`⇒ 2X=[[5+3 2+6],[0+0 9-1]]`
`⇒2X=[[8 8],[0 8]]`
`⇒X=1/2 [[8 8],[0 8]]`
`⇒X=[[4 4],[0 4]]`
Now,
`(X+Y)-(X-Y)=[[5 2],[0 9]]-[[ 3 6],[ 0 -1]]`
`⇒X+Y-X+Y=[[5-3 2-6],[0-0 9+1]]`
`⇒ 2Y=[[2 -4],[0 10]]`
`⇒ Y = 1/2[[2 -4],[0 10]]`
`⇒ Y=[[1 -2],[0 5]]`
`∴x=[[4 4],[0 4]]`and `Y=[[1 -2],[0 5]]`
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