Answer
$\begin{bmatrix} -2&14\\ \frac{3}{2}&- \frac{3}{2}\\ \frac{27}{2}& \frac{57}{2} \end{bmatrix}$
Work Step by Step
Step 1. List the matrices needed:
$\begin{array} \\F=\\ \end{array}
\begin{bmatrix} 4&0&2\\ -1&1&0\\7&5&0 \end{bmatrix},
\begin{array} \\C=\\ \end{array}
\begin{bmatrix} 1/2&3\\ 2&3/2\\-2&1 \end{bmatrix}$
Step 2. Perform the operation:
$\begin{array} \\FC=\\ \end{array}
\begin{bmatrix} 4&0&2\\ -1&1&0\\7&5&0 \end{bmatrix}
\begin{bmatrix} 1/2&3\\ 2&3/2\\-2&1 \end{bmatrix}
=\begin{bmatrix} 2+0-4&12+0+2\\ -1/2+2+0&-3+3/2+0\\7/2+10+0&21+15/2+0 \end{bmatrix}
=\begin{bmatrix} -2&14\\ \frac{3}{2}&- \frac{3}{2}\\ \frac{27}{2}& \frac{57}{2} \end{bmatrix}$
