Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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if 2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]] , find (x−y). - Mathematics

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if `2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]]` , find (xy).

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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=0y=8

and

2x+1=5  2x=4  x=2

So, (xy) = [2 − (−8)] = 2 + 8 = 10

Thus, the value of (xy) is 10.

 

 

Concept: Equality of Matrices
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