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Question
f X − Y =`[[1 1 1],[1 1 0],[1 0 0]]` and X + Y = `[[3 5 1],[-1 1 1],[11 8 0]]`find X and Y.
Solution
Here,
X−Y+X+Y= `[[1,1,1],[1,1,0],[1,0,0]]+` `[[3,5,1],[-1,1,4],[11,8,0]]`
`⇒ 2X= [[1+3,1+5,1+1],[1-1,1+1 ,0+1 ],[1+11,0+8,0+0]]`
`⇒ 2X =[[4,6 ,2],[0,2,4],[12,8,0]]`
`⇒ X = 1/2 [[4 6 2],[0 2 4],[12 8 0]]`
`⇒ X=[[2 3 1],[0 1 2],[6 4 0]]`
Now,
`(X-Y)-(X+Y)=[[1 1 1],[1 1 0],[1 0 0]]`-`[[3 5 1],[-1 1 1],[11 8 0]]`
⇒X−Y−X−Y=`[[1-3 1-5 1-1 ],[1+1 1-1 0-4],[1-11 0-8 0-0]]`
⇒−2Y= `[[-2 -4 0],[2 0 -4],[-10 -8 0]]`
⇒Y=−`1/2` `[[-2 -4 0],[2 0 -4],[-10 -8 0]]`
⇒Y=`[[1 2 0],[-1 0 2],[5 4 0]]`
`∴ X= [[2 3 1],[0 1 2],[6 4 0]]` And Y = `=[[1 2 0],[-1 0 2],[5 4 0]]`
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