Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}2&1&3\\4&-1&0\\-7&2&1\end{bmatrix}\)
Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}2&1&3\\4&-1&0\\-7&2&1\end{bmatrix}\)
Solution and Explanation
Let A=\(\begin{bmatrix}2&1&3\\4&-1&0\\-7&2&1\end{bmatrix}\)
We have IAI=2(-1-0)-1(4-0)+3(8-7)
=-2-4+3
=-3
Now A11=-1-0=-1, A12=-(4-0), A13=8-7=1
A21=-(1-6)=5, A22=2+21=23, A23=-(-(4+7)=-11
A31=0+3=3, A32=-(0-12)=12,A33=-2-4=-6
therefore adj A=\(\begin{bmatrix}-1&5&3\\-4&23&12\\1&-11&-6\end{bmatrix}\)
so A-1=\(\frac{1}{\mid A\mid}\)adj A=\(-\frac{1}{3}\) \(\begin{bmatrix}-1&5&3\\-4&23&12\\1&-11&-6\end{bmatrix}\)
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