Answer:
The product of the two matrices is: [tex]\begin{pmatrix} 7 \\ 4\\ 2 \\\end{pmatrix}[/tex]
Step-by-Step Explanation:
Matrix multiplication is not done element wise.
Two matrices 'A' and 'B' are said be compatible to multiplication iff A is of the size [tex]$ m \times n $[/tex] and B is of the size [tex]$ n \times p $[/tex].
The product AB would be of the size [tex]$ m \times p $[/tex].
Here, the size of the first matrix is [tex]$ 3 \times 3 $[/tex]. Second matrix is [tex]$ 3 \times 1 $[/tex]. Therefore, the resultant matrix would be: [tex]$ 3 \times 1 $[/tex].
Now, [tex] \begin{pmatrix}3 & 6 & 1 \\2 & 4 & 0 \\0 & 6 & 2\end{pmatrix}[/tex] [tex]$ \times \begin{pmatrix} 2 \\ 0 \\ 1 \\\end{pmatrix}[/tex]
[tex]= \begin{bmatrix}3(2) + 6(0) + 1(1) \\2(2) + 4(0) + 0(1) \\0(2) + 6(0) + 1(2)\end{bmatrix}[/tex]
[tex]$ = \begin{bmatrix}6 + 0 + 1 \\4 + 0 + 0\\0 + 0 + 2\end{bmatrix}[/tex]
Therefore, the product is: [tex]\begin{pmatrix} 7 \\ 4\\ 2 \\\end{pmatrix}[/tex].
