Answer
$\begin{bmatrix} -\frac{7}{2}&10\\ 1&-\frac{9}{2}\\ \end{bmatrix} $
Work Step by Step
Step 1. List the matrices needed:
$\begin{array} \\B=\\ \end{array}
\begin{bmatrix} 1&2&4\\ -2&1&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} \\BC=\\ \end{array}
\begin{bmatrix} 1&2&4\\ -2&1&0 \end{bmatrix}
\begin{bmatrix} 1/2&3\\ 2&3/2\\-2&1 \end{bmatrix}=\begin{bmatrix} (1/2+4-8)&(3+3+4)\\ (-1+2+0)&(-6+3/2+0)\\ \end{bmatrix}=\begin{bmatrix} -\frac{7}{2}&10\\ 1&-\frac{9}{2}\\ \end{bmatrix} $
