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.

Answer 1

\[\]

\[Given: \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\begin{bmatrix}3 & 1 \\ 2 & 5\end{bmatrix} = \begin{bmatrix}7 & 11 \\ k & 23\end{bmatrix}\]

\[ \Rightarrow \begin{bmatrix}3 + 4 & 1 + 10 \\ 9 + 8 & 3 + 20\end{bmatrix} = \begin{bmatrix}7 & 11 \\ k & 23\end{bmatrix}\]

\[ \Rightarrow \begin{bmatrix}7 & 11 \\ 17 & 23\end{bmatrix} = \begin{bmatrix}7 & 11 \\ k & 23\end{bmatrix}\]

The corresponding elements of two equal matrices are equal .

\[ \therefore k = 17\]