Answer
$\begin{bmatrix}-1&2\\-5&4\end{bmatrix}$
Work Step by Step
We are given the matrices:
$B=\begin{bmatrix}1&-1\\2&1\end{bmatrix}$
$C=\begin{bmatrix}1&2\\-1&3\end{bmatrix}$
Compute $BC-3B$:
$BC-3B=\begin{bmatrix}1&-1\\2&1\end{bmatrix}\begin{bmatrix}1&2\\-1&3\end{bmatrix}-3\begin{bmatrix}1&-1\\2&1\end{bmatrix}$
$=\begin{bmatrix}1+1&2-3\\2-1&4+3\end{bmatrix}-\begin{bmatrix}3&-3\\6&3\end{bmatrix}$
$=\begin{bmatrix}2&-1\\1&7\end{bmatrix}-\begin{bmatrix}3&-3\\6&3\end{bmatrix}$
$=\begin{bmatrix}2-3&-1-(-3)\\1-6&7-3\end{bmatrix}$
$=\begin{bmatrix}-1&2\\-5&4\end{bmatrix}$
