Question

If $\left[\begin{array}{cc}2& 3\\ 5& 7\end{array}\right]\left[\begin{array}{cc}1& -3\\ -2& 4\end{array}\right]=\left[\begin{array}{cc}-4& 6\\ -9& x\end{array}\right]$, write the value of $x$.

Answer 1

$\left[\begin{array}{cc}2& 3\\ 5& 7\end{array}\right]\left[\begin{array}{cc}1& -3\\ -2& 4\end{array}\right]=\left[\begin{array}{cc}-4& 6\\ -9& x\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}2-6& -6+12\\ 5-14& -15+28\end{array}\right]=\left[\begin{array}{cc}-4& 6\\ -9& x\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}-4& 6\\ -9& 13\end{array}\right]=\left[\begin{array}{cc}-4& 6\\ -9& x\end{array}\right]$

$\Rightarrow x=13$

Hence, the answer is $13.$