Answer
$\begin{bmatrix} -12&12\\ 4&2\\20&34 \end{bmatrix}$
Work Step by Step
Step 1. List the matrices needed:
$\begin{array} \\C=\\ \end{array}
\begin{bmatrix} 1/2&3\\ 2&3/2\\-2&1 \end{bmatrix},
\begin{array} \\D=\\ \end{array}
\begin{bmatrix} 1&4\\ 0&-1\\2&0 \end{bmatrix},
\begin{array} \\F=\\ \end{array}
\begin{bmatrix} 4&0&2\\ -1&1&0\\7&5&0 \end{bmatrix} $
Step 2. Perform the operation:
$\begin{array} \\2C-D=\\ \end{array}
\begin{bmatrix} 1&6\\ 4&3\\-4&2 \end{bmatrix}
\begin{array} \\-\\ \end{array}
\begin{bmatrix} 1&4\\ 0&-1\\2&0 \end{bmatrix}
=\begin{bmatrix} 0&2\\ 4&4\\-6&2 \end{bmatrix} $
Step 3. Perform the operation:
$\begin{array} \\F(2C-D)=\\ \end{array}
\begin{bmatrix} 4&0&2\\ -1&1&0\\7&5&0 \end{bmatrix}
\begin{bmatrix} 0&2\\ 4&4\\-6&2 \end{bmatrix}
=\begin{bmatrix} 0+0-12&8+0+4\\ 0+4+0&-2+4+0\\0+20+0&14+20+0 \end{bmatrix}
=\begin{bmatrix} -12&12\\ 4&2\\20&34 \end{bmatrix}$
