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 value of $x.$

Answer 1

Consider,

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

$\left(\begin{array}{cc}2\times 1+3\times -2& 2\times -3+3\times 4\\ 5\times 1+7\times -2& 5\times -3+7\times 4\end{array}\right)=\left(\begin{array}{cc}-4& 6\\ -9& x\end{array}\right)$

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

$\left(\begin{array}{cc}-4& 6\\ -9& 13\end{array}\right)=\left(\begin{array}{cc}-4& 6\\ -9& x\end{array}\right)$

Equating the matrices we get the value of $x$ that is $x=13$

Hence $x=13$.