Answer
$\begin{bmatrix} -\frac{1}{2}&\frac{11}{2}\\ \frac{15}{4}&-\frac{3}{2}\\-\frac{1}{2}&1 \end{bmatrix}$
Work Step by Step
Step 1. List the matrices needed:
$\begin{array} \\C=\\ \end{array}
\begin{bmatrix} 1/2&3\\ 2&3/2\\-2&1 \end{bmatrix},
\begin{array} \\D=\\ \end{array}
\begin{bmatrix} 1&4\\ 0&-1\\2&0 \end{bmatrix},
\begin{array} \\E=\\ \end{array}
\begin{bmatrix} 2&-1\\ -1/2&1 \end{bmatrix}$
Step 2. Perform the operation:
$\begin{array} \\C+D=\\ \end{array}
\begin{bmatrix} 1/2&3\\ 2&3/2\\-2&1 \end{bmatrix}
\begin{array} \\+\\ \end{array}
\begin{bmatrix} 1&4\\ 0&-1\\2&0 \end{bmatrix}
=\begin{bmatrix} 3/2&7\\ 2&1/2\\0&1 \end{bmatrix}$
Step 3. Perform the operation:
$\begin{array} \\(C+D)E=\\ \end{array}
\begin{bmatrix} 3/2&7\\ 2&1/2\\0&1 \end{bmatrix}
\begin{bmatrix} 2&-1\\ -1/2&1 \end{bmatrix}
=\begin{bmatrix} 3-7/2&-3/2+7\\ 4-1/4&-2+1/2\\0-1/2&0+1 \end{bmatrix}
=\begin{bmatrix} -\frac{1}{2}&\frac{11}{2}\\ \frac{15}{4}&-\frac{3}{2}\\-\frac{1}{2}&1 \end{bmatrix}$
