Given:
The matrix multiplication
[tex]\begin{bmatrix}1&4\\3&2\end{bmatrix}\begin{bmatrix}8\\1\end{bmatrix}[/tex]
To find:
The value of [tex]a_{11}[/tex] in the resulting matrix.
Solution:
We have,
[tex]\begin{bmatrix}1&4\\3&2\end{bmatrix}\begin{bmatrix}8\\1\end{bmatrix}[/tex]
It can be written as
[tex]\begin{bmatrix}1&4\\3&2\end{bmatrix}\begin{bmatrix}8\\1\end{bmatrix}=\begin{bmatrix}1\times 8+4\times 1\\3\times 8+2\times 1\end{bmatrix}[/tex]
[tex]\begin{bmatrix}1&4\\3&2\end{bmatrix}\begin{bmatrix}8\\1\end{bmatrix}=\begin{bmatrix}8+4\\24+2\end{bmatrix}[/tex]
[tex]\begin{bmatrix}1&4\\3&2\end{bmatrix}\begin{bmatrix}8\\1\end{bmatrix}=\begin{bmatrix}12\\26\end{bmatrix}[/tex]
The element of first row and first column is 12. So, the value of [tex]a_{11}[/tex] is 12.
Therefore, the correct option is B.
