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Using elementary transformations, find the inverse of the matrix `[[1,3],[2,7]]`

Text Solution

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`A=[[1,3​],[2,7]​]`
`[A/I]=[[1,3​,|,1,0]​,[2,7​,|,0,1]​]`
Applying`R_2​−2R_1`
=`[[1,3​,|,1,0]​,[0,1​,|,-2,1]​]`
apllying`R_1​−3R_2`
​`[[1,0​,|,1,-3]​,[0,1​,|,0,1]​]`
∴`A^(−1)=[[1,-3],[0,1]]`
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