Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}1&-1&2\\0&2&-3\\3&-2&4\end{bmatrix}\)
Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}1&-1&2\\0&2&-3\\3&-2&4\end{bmatrix}\)
Solution and Explanation
Let A=\(\begin{bmatrix}1&-1&2\\0&2&-3\\3&-2&4\end{bmatrix}\)
By expanding along C1,we have :
IAI=1(8-6)-0+3(3-4)=2-3=-1
Now A11=8-6=2, A12=-(0+9)=-9, A13=0-6=-6
A21=-(-4+4)=0, A22=4-6=-2, A23=-(-2+3)=-1
A31=3-4=-1, A32=-(-3-0)=3, A33=2-0=2
so adj A=\(\begin{bmatrix}2&0&-1\\-9&-2&3\\-6&-1&2\end{bmatrix}\)
so A-1=\(\frac{1}{\mid A \mid}\)adj A=- \(\begin{bmatrix}2&0&-1\\-9&-2&3\\-6&-1&2\end{bmatrix}\)
=\(\begin{bmatrix}-2&0&1\\9&2&-3\\6&1&-2\end{bmatrix}\)
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