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Question
if `2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]]` , find (x−y).
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Solution
It is given that `2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]].`
Let us simplify the left hand side as below:
`[[2xx3,2xx4],[2xx5,2x]]+[[1,y],[0,1]]=[[7,0],[10,5]]`
`[[6,8],[10,2x]]+[[1,y],[0,1]]=[[7,0],[10,5]]`
`[[6+1,8+y],[10,2x+1]]=[[7,0],[10,5]]`
`[[7,8+y],[10,2x+1]]=[[7,0],[10,5]]`
Two matrices are equal if and only if their corresponding entries are equal.
So, equating the corresponding entries, we get:
8+y=0⇒y=−8
and
2x+1=5 ⇒2x=4 ⇒x=2
So, (x − y) = [2 − (−8)] = 2 + 8 = 10
Thus, the value of (x − y) is 10.
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