[tex] \left[\begin{array}{ccc}3&6\\-2&5\end{array}\right] \cdot \left[\begin{array}{ccc}4\\a\end{array}\right] = \left[\begin{array}{ccc}30\\7\end{array}\right] \\
\left[\begin{array}{ccc}3\cdot4+6\cdot a\\-2\cdot4+5\cdot a\end{array}\right] = \left[\begin{array}{ccc}30\\7\end{array}\right] \\
\left[\begin{array}{ccc}12+6a\\-8+5a\end{array}\right] = \left[\begin{array}{ccc}30\\7\end{array}\right] \\\\
12+6a=30\\
-8+5a=7\\\\
6a=18\\
5a=15\\\\
a=3\\
a=3\\\\
\boxed{a=3}[/tex]
I'm not good at this stuff. There may a quicker and better way to solve it.
