Question

What is the product?

Answer 1

`\begin{bmatrix}7\\ 4\\ 2\end{bmatrix}`

Explanation:

We have the product,
`\begin{bmatrix} 3& 6& 1\\ 2& 4& 0\\ 0& 6& 2\end{bmatrix}* \begin{bmatrix}2\\ 0\\ 1\end{bmatrix}`.

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,

`\begin{bmatrix} 3& 6& 1\\ 2& 4& 0\\ 0&6&2\end{bmatrix}* \begin{bmatrix}2\\ 0\\ 1\end{bmatrix}`

⇒
`\begin{bmatrix}3* 2+6* 0+1* 1\\ 2* 2+4* 0+0* 1\\ 0* 2+6* 0+2* 1\end{bmatrix}`

⇒
`\begin{bmatrix}7\\ 4\\ 2\end{bmatrix}`.

Thus, the resulting product is
`\begin{bmatrix}7\\ 4\\ 2\end{bmatrix}`.