Find the inverse of each of the matrices (if it exists). \(\begin{bmatrix}1&0&0\\3&3&0\\5&2&-1\end{bmatrix}\)
Find the inverse of each of the matrices (if it exists). \(\begin{bmatrix}1&0&0\\3&3&0\\5&2&-1\end{bmatrix}\)
Solution and Explanation
Let A=\(\begin{bmatrix}1&0&0\\3&3&0\\5&2&-1\end{bmatrix}\)
we have IAI=1(-3-0)-0+0=-3
now A11=-3-0=-3, A12=-(-3-0)=3, A13=6-15=9
A21=-(0-0)=0, A22=-1-0=-1,A23=-(2-0)=-2
A31=0-0=0,A32=-(0-0)=0,A33=3-0=3
therefore adj A=\(\begin{bmatrix}-3&0&0\\3&-1&0\\-9&-2&3\end{bmatrix}\)
so A-1=\(\frac{1}{\mid A \mid}\)adj A=\(-\frac{1}{3}\)\(\begin{bmatrix}-3&0&0\\3&-1&0\\-9&-2&3\end{bmatrix}\)
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