Question

What is the product?
3 6 1 2
2 4 0x0
0 6 2 1

Answer 1

D is the correct answer

Explanation:

edge 2023

Answer 2

The product of the two matrices is:
`\begin{pmatrix}  7 \\  4\\  2 \\\end{pmatrix}`

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
`$ m * n $` and B is of the size
`$ n * p $`.

The product AB would be of the size
`$ m * p $`.

Here, the size of the first matrix is
`$ 3 * 3 $`. Second matrix is
`$ 3 * 1 $`. Therefore, the resultant matrix would be:
`$ 3 * 1 $`.

Now,
`\begin{pmatrix}3 & 6 & 1 \\2 & 4 & 0 \\0 & 6 & 2\end{pmatrix}`
`$ * \begin{pmatrix}  2 \\  0 \\  1 \\\end{pmatrix}`

`= \begin{bmatrix}3(2) +  6(0) + 1(1) \\2(2) + 4(0) + 0(1) \\0(2) + 6(0) + 1(2)\end{bmatrix}`

`$ = \begin{bmatrix}6 + 0 + 1 \\4 + 0 + 0\\0 + 0 + 2\end{bmatrix}`

Therefore, the product is:
`\begin{pmatrix}  7 \\  4\\  2 \\\end{pmatrix}`.