Question

$If\left[\begin{array}{c}1\\ 3\end{array}\begin{array}{c}2\\ 4\end{array}\right]\left[\begin{array}{c}3\\ 2\end{array}\begin{array}{c}1\\ 5\end{array}\right]=\left[\begin{array}{c}7\\ k\end{array}\begin{array}{c}11\\ 23\end{array}\right]$ then writ the value of $k$

Answer 1

$\stackrel{⟶}{\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]}\times \left[\begin{array}{cc}3& 1\\ 2& 5\end{array}\right]\downarrow =\left[\begin{array}{cc}7& 11\\ 4& 23\end{array}\right]$

$or,\left[\begin{array}{cc}3+4& 1+10\\ 9+8& 3+20\end{array}\right]=\left[\begin{array}{cc}7& 11\\ 4& 23\end{array}\right]$

$or,\left[\begin{array}{cc}7& 11\\ 17& 23\end{array}\right]=\left[\begin{array}{cc}7& 11\\ 4& 23\end{array}\right]$

Equating both sides, $k=17$