The inverse of the matrix begin{bmatrix} 5 & | vedclass

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(A) Let $A = \begin{bmatrix} 5 & -2 \ 3 & 1 \end{bmatrix}$.First,we calculate the determinant of $A$:$|A| = (5)(1) - (-2)(3) = 5 + 6 = 11$.Next,we fi

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$\frac{1}{11} \begin{bmatrix} 1 & 2 \ -3 & 5 \end{bmatrix}$

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(A) Let $A = \begin{bmatrix} 5 & -2 \ 3 & 1 \end{bmatrix}$.First,we calculate the determinant of $A$:$|A| = (5)(1) - (-2)(3) = 5 + 6 = 11$.Next,we find the adjoint of $A$,denoted as $adj(A)$. For a $2 	imes 2$ matrix $\begin{bmatrix} a & b \ c & d \end{bmatrix}$,the adjoint is $\begin{bmatrix} d & -b \ -c & a \end{bmatrix}$.$adj(A) = \begin{bmatrix} 1 & 2 \ -3 & 5 \end{bmatrix}$.The inverse of the matrix is given by $A^{-1} = \frac{1}{|A|} adj(A)$.$A^{-1} = \frac{1}{11} \begin{bmatrix} 1 & 2 \ -3 & 5 \end{bmatrix}$.

The inverse of the matrix $\begin{bmatrix} 5 & -2 \\ 3 & 1 \end{bmatrix}$ is

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