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  4. m[-3 4]+n[4 -3]=[10 -11]⇒ 3 m+7 n=

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Q. $m\begin{bmatrix}-3 & 4\end{bmatrix}+n\begin{bmatrix}4 & -3\end{bmatrix}=\begin{bmatrix}10 & -11\end{bmatrix}\Rightarrow 3 \,m+7 n=$

Solution:

$m\begin{bmatrix}-3 & 4\end{bmatrix}+n\begin{bmatrix}4 & -3\end{bmatrix}=\begin{bmatrix}10 & -11\end{bmatrix}$
$ \Rightarrow -3 \,m+4\,n=10,4 \,m-3 \,n=-11$
$ \Rightarrow m=-2, n=1$
$\therefore 3\, m+7 \,n=-6+7=1$