Find the inverse of the matrix,if it exists: | vedclass

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(A) Let $A = \left[\begin{array}{ll}3 & 1 \ 5 & 2\end{array}ight]$.First,we find the determinant of $A$:$|A| = (3 	imes 2) - (1 	imes 5) = 6 - 5

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$A^{-1}=\left[\begin{array}{cc}2 & -1 \ -5 & 3\end{array}ight]$

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(A) Let $A = \left[\begin{array}{ll}3 & 1 \ 5 & 2\end{array}ight]$.First,we find the determinant of $A$:$|A| = (3 	imes 2) - (1 	imes 5) = 6 - 5 = 1$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The formula for the inverse of a $2 	imes 2$ matrix $\left[\begin{array}{ll}a & b \ c & d\end{array}ight]$ is $\frac{1}{|A|} \left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Applying this to matrix $A$:$A^{-1} = \frac{1}{1} \left[\begin{array}{cc}2 & -1 \ -5 & 3\end{array}ight] = \left[\begin{array}{cc}2 & -1 \ -5 & 3\end{array}ight]$.

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}3 & 1 \\ 5 & 2\end{array}\right]$

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