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.

Concept: Equality of Matrices

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