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If A = [[1,-2,3],[0,-1,4],[-2,2,1]] ,find (A')-1 - CBSE (Commerce) Class 12 - Mathematics

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Question

 

If A = `[[1,-2,3],[0,-1,4],[-2,2,1]]` ,find (A')-1

 

Solution

`A=[[1,-2,3],[0,-1,4],[-2,2,1]]`

`=>A'=[[1,0,-2],[-2,-1,2],[3,4,1]]`

Now 

`|A'|=|[1,0,-2],[-2,-1,2],[3,4,1]|=1(-1-8)-0(-2-6)-2(-8+3)=-9+10=1ne 0`

`adjA'=[[-9,-8,-2],[8,7,2],[-5,-4,-1]]`

`therefore (A')^-1="adjA'"/|A'|`

`=>(A')^-1=[[-9,-8,-2],[8,7,2],[-5,-4,-1]]`

 

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Solution If A = [[1,-2,3],[0,-1,4],[-2,2,1]] ,find (A')-1 Concept: Inverse of a Matrix by Elementary Operations.
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