Given:
The matrix multiplication
[tex]\begin{bmatrix}4&5&6\\1&2&3\end{bmatrix}\begin{bmatrix}10\\20\\30\end{bmatrix}[/tex]
To find:
The order of resulting matrix.
Solution:
We know that, if order of first matrix is [tex]m_1\times n_1[/tex] and the order of second matrix is [tex]m_2\times n_2[/tex], then the order of these two matrices is [tex]m_1\times n_2[/tex].
We have,
[tex]\begin{bmatrix}4&5&6\\1&2&3\end{bmatrix}\begin{bmatrix}10\\20\\30\end{bmatrix}[/tex]
Here, the order of first matrix is [tex]2\times 3[/tex] and the order of the second matrix is [tex]3\times 1[/tex]. So, the order of the second matrix is [tex]2\times 1[/tex]. It is also written are 2 by 1.
Therefore, the correct option is A.
