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