The element in the third row and first column | vedclass

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(C) Let $A = \left[\begin{array}{ccc}1 & -3 & 2 \ -3 & 3 & -1 \ 2 & -1 & 0\end{array}ight]$.First,we calculate the determinant $|A|$:$|A| = 1(0 -

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$3$

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(C) Let $A = \left[\begin{array}{ccc}1 & -3 & 2 \ -3 & 3 & -1 \ 2 & -1 & 0\end{array}ight]$.First,we calculate the determinant $|A|$:$|A| = 1(0 - 1) - (-3)(0 - (-2)) + 2(3 - 6)$$|A| = 1(-1) + 3(2) + 2(-3) = -1 + 6 - 6 = -1$.The element in the third row and first column of $A^{-1}$ is given by $\frac{C_{13}}{|A|}$,where $C_{13}$ is the cofactor of the element in the first row and third column of $A$.$C_{13} = (-1)^{1+3} \left|\begin{array}{cc}-3 & 3 \ 2 & -1\end{array}ight| = 1(3 - 6) = -3$.Therefore,the element in the third row and first column of $A^{-1}$ is $\frac{-3}{-1} = 3$.

The element in the third row and first column of the inverse of the matrix $\left[\begin{array}{ccc}1 & -3 & 2 \\ -3 & 3 & -1 \\ 2 & -1 & 0\end{array}\right]$ is

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