Answer:
The product of given matrix is [tex]AB=\begin{pmatrix}7\\ 4\\ 2\end{pmatrix}[/tex]
Step-by-step explanation:
Given : Two matrix
[tex]A=\begin{pmatrix}3&6&1\\ 2&4&0\\ 0&6&2\end{pmatrix}[/tex]
and [tex]B=\begin{pmatrix}2\\ \:0\\ \:1\end{pmatrix}[/tex]
We have to find the product of given matrix
[tex]AB=\begin{pmatrix}3&6&1\\ 2&4&0\\ 0&6&2\end{pmatrix}\begin{pmatrix}2\\ 0\\ 1\end{pmatrix}[/tex]
Multiply the rows of first matrix by the columns of second matrix , we have,
[tex]\begin{pmatrix}3&6&1\end{pmatrix}\begin{pmatrix}2\\ 0\\ 1\end{pmatrix}=3\cdot \:2+6\cdot \:0+1\cdot \:1[/tex]
[tex]\begin{pmatrix}2&4&0\end{pmatrix}\begin{pmatrix}2\\ 0\\ 1\end{pmatrix}=2\cdot \:2+4\cdot \:0+0\cdot \:1[/tex]
[tex]\begin{pmatrix}0&6&2\end{pmatrix}\begin{pmatrix}2\\ 0\\ 1\end{pmatrix}=0\cdot \:2+6\cdot \:0+2\cdot \:1[/tex]
[tex]=\begin{pmatrix}3\cdot \:2+6\cdot \:0+1\cdot \:1\\ 2\cdot \:2+4\cdot \:0+0\cdot \:1\\ 0\cdot \:2+6\cdot \:0+2\cdot \:1\end{pmatrix}[/tex]
On , simplifying , we get,
[tex]AB=\begin{pmatrix}7\\ 4\\ 2\end{pmatrix}[/tex]
Thus, the product of given matrix is [tex]AB=\begin{pmatrix}7\\ 4\\ 2\end{pmatrix}[/tex]
Answer: The product is [tex]\left[\begin{array}{ccc}7\\4\\2\end{array}\right][/tex]
Step-by-step explanation:
Since we have given that
[tex]\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right] \times \left[\begin{array}{ccc}2\\0\\1\end{array}\right][/tex]
As we know the way to multiply in case of matrices.
Since the order of first matrix is 3×3
And the order of second matrix is 3 × 1
So, the order of the product matrix is 3 × 1
So, the product becomes
[tex]\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right] \times \left[\begin{array}{ccc}2\\0\\1\end{array}\right]\\\\=\left[\begin{array}{ccc}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{array}\right] \\\\=\left[\begin{array}{ccc}7\\4\\2\end{array}\right][/tex]
Hence, the product is [tex]\left[\begin{array}{ccc}7\\4\\2\end{array}\right][/tex]
