Question

HELP!!!

What is the product?

Answer 1

(b)
`\left[ \begin{array}{c c c} 1 & 26 & 7\end{array} \right]`

Explanation:

First, we can determine the dimensions of the matrix that results from this multiplication by looking at the dimensions of each of its matrix factors:

( in the form
`\text{rows} * \text{columns}` )

1st matrix →
`1 * 3`,
`3* 3` ← 2nd matrix

To get the dimensions of the resulting matrix, we can take out the inner two dimensions to get the number of rows from the 1st matrix and the number of columns from the 2nd matrix (which become the rows and columns of the resulting matrix).

`1* \\ot 3, \ \\ot3 * 3 \implies 1* 3`

So, the resulting matrix will have 1 row and 3 columns. Using this knowledge, we can immediately identify (b) and (c) as possible correct answer choices.

We can find the values in the resulting matrix by multiplying the rows of the first matrix by the columns of the second matrix:

`\left[ \begin{array}{c c c}\left(-1\right)\cdot \:3+2\cdot \:2+4\cdot \:0&\left(-1\right)\cdot \:6+2\cdot \:4+4\cdot \:6&\left(-1\right)\cdot \:1+2\cdot \:0+4\cdot \:2\end{array} \right]`

`\boxed{\left[ \begin{array}{c c c} 1 & 26 & 7\end{array} \right]}`

So, (b) [ 1 26 7 ] is the correct answer.