If $\left(\begin{array}{cc}3& -2\\ -1& 2\end{array}\right)\left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)=\left(\begin{array}{c}11\\ -5\end{array}\right)$ then 3x + 7y =

$$\begin{gathered} \left[\begin{array}{cc}3& -2\\ -1& 2\end{array}\right] \left[\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right]=\left[\begin{array}{c}11\\ -5\end{array}\right] \\ \left[\begin{array}{c}3\mathrm{x}-2\mathrm{y}\\ -\mathrm{x}+2\mathrm{y}\end{array}\right]=\left[\begin{array}{c}4\\ -5\end{array}\right] \\ \therefore 3\mathrm{x}-2\mathrm{y}=11, -\mathrm{x}+2\mathrm{y}=-5 \end{gathered}$$

on solving above two equations, we get

$$\begin{gathered} \mathrm{x}=3, \mathrm{y}=-1 \\ \therefore 3\mathrm{x}+7\mathrm{y}=9-7 \\ =2 \end{gathered}$$