Answer:
[tex]\begin{bmatrix}7\\ 4\\ 2\end{bmatrix}[/tex]
Step-by-step explanation:
We have the product, [tex]\begin{bmatrix} 3& 6& 1\\ 2& 4& 0\\ 0& 6& 2\end{bmatrix}\times \begin{bmatrix}2\\ 0\\ 1\end{bmatrix}[/tex].
As, we have the product of a 3×3 and 3×1 matrix, the resultant matrix will be of order 3×1.
So, we get,
[tex]\begin{bmatrix} 3& 6& 1\\ 2& 4& 0\\ 0&6&2\end{bmatrix}\times \begin{bmatrix}2\\ 0\\ 1\end{bmatrix}[/tex]
⇒ [tex]\begin{bmatrix}3\times 2+6\times 0+1\times 1\\ 2\times 2+4\times 0+0\times 1\\ 0\times 2+6\times 0+2\times 1\end{bmatrix}[/tex]
⇒ [tex]\begin{bmatrix}7\\ 4\\ 2\end{bmatrix}[/tex].
Thus, the resulting product is [tex]\begin{bmatrix}7\\ 4\\ 2\end{bmatrix}[/tex].
