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(A) Let $A = \left[\begin{array}{cc}3 & -1 \ -4 & 2\end{array}ight]$.First,calculate the determinant of $A$:$|A| = (3)(2) - (-1)(-4) = 6 - 4 = 2$.S

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let $A = \left[\begin{array}{cc}3 & -1 \ -4 & 2\end{array}ight]$.First,calculate the determinant of $A$:$|A| = (3)(2) - (-1)(-4) = 6 - 4 = 2$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The formula for the inverse of a $2 	imes 2$ matrix $\left[\begin{array}{cc}a & b \ c & d\end{array}ight]$ is $\frac{1}{ad-bc} \left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Applying this to matrix $A$:$A^{-1} = \frac{1}{2} \left[\begin{array}{cc}2 & 1 \ 4 & 3\end{array}ight] = \left[\begin{array}{cc}1 & 1/2 \ 2 & 3/2\end{array}ight]$.

Find the inverse of the matrix,if it exists: $\left[\begin{array}{cc}3 & -1 \\ -4 & 2\end{array}\right]$

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