Find the inverse of the matix, `A=[[2,-3],[-4,7]]`.

1.	Find the inverse of the matix, `A=[[2,-3],[-4,7]]`.
Answer» We have `\|A\|=\|(2,-3),(-4,7)\|=(14-12)=2!=0` So, `A_(1)` exists. The cofactors of the elements of `\|A\|` are given by `A_(11)=7,A_(12)=-(-4)=4,` `A_(21)=-(-3)=3, A_(22)=2.` `:." "(adj A)=[[7,4],[3,2]]=[[7,3],[4,2]].` `Hence,A^(-1)=1/\|A\|.(adj A)` `=1/2.[[7,3],[4,2]]=[[7/2,3/2],[2,1]]`

Discussion

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