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