Answer
$\begin{bmatrix}\dfrac{7}{2}&2\\\dfrac{9}{2}&3\\-5&-\dfrac{7}{2}\end{bmatrix}$
Work Step by Step
We are given the matrices:
$$A=\begin{bmatrix}-1&2\\-3&0\\4&1\end{bmatrix},\text{ }B=\begin{bmatrix}3&2\\-2&-1\end{bmatrix}, \text{ }C=\begin{bmatrix}-4&5\\1&0\end{bmatrix}.$$
Calculate $-\dfrac{1}{2}AB$:
$$\begin{align*}
-\dfrac{1}{2}AB&=\begin{bmatrix}-1&2\\-3&0\\4&1\end{bmatrix}\cdot\begin{bmatrix}3&2\\-2&-1\end{bmatrix}\\
&=-\dfrac{1}{2}\begin{bmatrix}-7&-4\\-9&-6\\10&7\end{bmatrix}\\
&=\begin{bmatrix}\dfrac{7}{2}&2\\\dfrac{9}{2}&3\\-5&-\dfrac{7}{2}\end{bmatrix}.
\end{align*}$$
