What is the product?
$
\left[\begin{array}{lll}
3 & 6 & 1 \\
2 & 4 & 0 \\
0 & 6 & 2
\end{array}\right] \times\left[\begin{array}{c}
2 \\
0 \\
1
\end{array}\right]
$
$\left[\begin{array}{c}13 \\ 9 \\ 10\end{array}\right]$
$\left[\begin{array}{lll}5 & 8 & 3 \\ 2 & 4 & 0 \\ 1 & 7 & 3\end{array}\right]$
$\left[\begin{array}{lll}6 & 12 & 2\end{array}\right]$

[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\times1\\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]Answer:

Step-by-step explanation:

Answer Link

msm555 msm555 · Answer 2 · 2024-05-05T22:20:25-04:00

Answer:

[tex] \sf \begin{bmatrix} 7 \\ 4 \\ 2 \end{bmatrix} [/tex]

Step-by-step explanation:

The product in this context refers to the result of matrix multiplication. Matrix multiplication involves multiplying each element of a row from the first matrix by the corresponding element of a column from the second matrix and summing the products.

Let the given matrices be:

[tex] \sf A = \begin{bmatrix} 3 & 6 & 1 \\ 2 & 4 & 0 \\ 0 & 6 & 2 \end{bmatrix} [/tex]

and

[tex] \sf B = \begin{bmatrix} 2 \\ 0 \\ 1 \end{bmatrix} [/tex]

The product [tex]\bold{\sf AB }[/tex] is calculated by taking the dot product of each row of matrix [tex]\bold{\sf A }[/tex] with the single column matrix [tex]\bold{\sf B }[/tex], resulting in a new matrix:

[tex] \sf AB = \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} = \begin{bmatrix} 7 \\ 4 \\ 2 \end{bmatrix} [/tex]

So, the product of the matrices [tex]\bold{\sf A }[/tex] and [tex]\bold{\sf B }[/tex] is the matrix:

[tex] \sf \begin{bmatrix} 7 \\ 4 \\ 2 \end{bmatrix} [/tex]