Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}-1&5\\-3&2\end{bmatrix}\)
Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}-1&5\\-3&2\end{bmatrix}\)
Solution and Explanation
Let A=\(\begin{bmatrix}-1&5\\-3&2\end{bmatrix}\)
IAI=-2+15=13
Now A11=2 ,A12=3, A21=-5, A22=-1
therefore adj A=\(\begin{bmatrix}2&-5\\3&1\end{bmatrix}\)
therefore A-1=\(\frac{1}{\mid A\mid}\)adj A=\(\frac{1}{13}\) \(\begin{bmatrix}2&-5\\3&1\end{bmatrix}\)
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