Answer
$$\left[ \begin {array}{cc} 6&-19\\ 10&7
\end {array} \right]=3\left[ \begin {array}{cc} 2&-3\\ 4&1
\end {array} \right]-2\left[ \begin {array}{cc} 0&5\\ 1&-2
\end {array} \right].$$
Work Step by Step
Assume the combination
$$\left[ \begin {array}{cc} 6&-19\\ 10&7
\end {array} \right]=a\left[ \begin {array}{cc} 2&-3\\ 4&1
\end {array} \right]+b\left[ \begin {array}{cc} 0&5\\ 1&-2
\end {array} \right].$$
We have the system
\begin{align*}
2a&=6\\
-3a+5b&=-19\\
4a+b&=10\\
a-2b&=7.
\end{align*}
We get the solution $$a=3, \quad b=-2.$$
Consequently,
$$\left[ \begin {array}{cc} 6&-19\\ 10&7
\end {array} \right]=3\left[ \begin {array}{cc} 2&-3\\ 4&1
\end {array} \right]-2\left[ \begin {array}{cc} 0&5\\ 1&-2
\end {array} \right].$$
