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Find the inverse \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \e...

Find the inverse $\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}$

A.

$\begin{vmatrix} 2 & -\frac{3}{2} \\ -3 & -\frac{5}{2} \end{vmatrix}$

B.

$\begin{vmatrix} 2 & -\frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}$

C.

$\begin{vmatrix} 2 & \frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}$

D.

$\begin{vmatrix} 2 & \frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}$

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Correct answer is B

Let A = $\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}$

Then |A| = $\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}$ = 20 - 18 = 2

Hence A-1 = $\frac{1}{|A|}\begin{pmatrix} 4 & -3 \\ -6 & 5 \end{pmatrix}$

= $\frac{1}{2}\begin{pmatrix} 4 & -3 \\ -6 & 5 \end{pmatrix}$

= $\begin{pmatrix} 4 \times 1/2 & -3 \times 1/2 \\ -6 \times 1/2 & 5 \times 1/2 \end{pmatrix}$

= $\begin{pmatrix} 2 & -\frac{3}{2} \\ -3 & \frac{5}{2} \end{pmatrix}$

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