Find the inverse of the matrix A = left[begin | vedclass

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Question

(A) Let $A = \left[\begin{array}{ll}2 & 3 \ 5 & 7\end{array}ight]$.First,we find the determinant of $A$:$|A| = (2 	imes 7) - (3 	imes 5) = 14 - 1

Vedclass · Accepted Answer

$A^{-1} = \left[\begin{array}{cc}-7 & 3 \ 5 & -2\end{array}ight]$

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(A) Let $A = \left[\begin{array}{ll}2 & 3 \ 5 & 7\end{array}ight]$.First,we find the determinant of $A$:$|A| = (2 	imes 7) - (3 	imes 5) = 14 - 15 = -1$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The inverse of a $2 	imes 2$ matrix $\left[\begin{array}{ll}a & b \ c & d\end{array}ight]$ is given by $\frac{1}{|A|} \left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Substituting the values:$A^{-1} = \frac{1}{-1} \left[\begin{array}{cc}7 & -3 \ -5 & 2\end{array}ight]$$A^{-1} = \left[\begin{array}{cc}-7 & 3 \ 5 & -2\end{array}ight]$.

Find the inverse of the matrix $A = \left[\begin{array}{ll}2 & 3 \\ 5 & 7\end{array}\right]$,if it exists.

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