Question

If $\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\left[\begin{array}{cc}3& 1\\ 2& 5\end{array}\right]=\left[\begin{array}{cc}7& 11\\ k& 23\end{array}\right]$, then write the value of k.

Answer 1

$$\begin{gathered} \mathrm{Given}:\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\left[\begin{array}{cc}3& 1\\ 2& 5\end{array}\right]=\left[\begin{array}{cc}7& 11\\ k& 23\end{array}\right] \\ \Rightarrow \left[\begin{array}{cc}3+4& 1+10\\ 9+8& 3+20\end{array}\right]=\left[\begin{array}{cc}7& 11\\ k& 23\end{array}\right] \\ \Rightarrow \left[\begin{array}{cc}7& 11\\ 17& 23\end{array}\right]=\left[\begin{array}{cc}7& 11\\ k& 23\end{array}\right] \\ \mathrm{The}\mathrm{corresponding}\mathrm{elements}\mathrm{of}\mathrm{two}\mathrm{equal}\mathrm{matrices}\mathrm{are}\mathrm{equal}. \\ \therefore k=17 \end{gathered}$$