Question

If $m\left[\begin{array}{cc}-3& 4\end{array}\right]+n\left[\begin{array}{cc}4& -3\end{array}\right]=\left[\begin{array}{cc}10& -11\end{array}\right]$, then find $m$ and $n$.

• A. $m=-2,n=1$
• B. $m=2,n=-1$
• C. $m=-2,n=-1$
• D. $m=2,n=1$

Answer 1

Answer: (A)

$m=-2,n=1$

Given, $m\left[\begin{array}{cc}-3& 4\end{array}\right]+n\left[\begin{array}{cc}4& -3\end{array}\right]=\left[\begin{array}{cc}10& -11\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}-3m+4n& 4m-3n\end{array}\right]=\left[\begin{array}{cc}10& -11\end{array}\right]$

By equating above matrices, we get

$-3m+4n=10⟹12m-16n=-40$ ......(1)

$4m-3n=-11⟹12m-9n=-33$ ......(2)

Solving equation 1 and 2, we get,

$-7n=-7$

$n=1$

And, $m=-2$