# How do you multiply ((1, 3)) with ((-1, 2, 2, 4))?

Apr 20, 2016

You can't.

#### Explanation:

Perhaps one of the following was intended:

Possibility 1
Multiply $\left(\left(1 , 3\right)\right)$ by $\left(\begin{matrix}- 1 & 2 \\ 2 & 4\end{matrix}\right)$
Remember we multiply "rows" by "columns"
There is only one row: $\left(\left(1 , 3\right)\right)$
but two columns: $\left(\begin{matrix}- 1 \\ 2\end{matrix}\right)$ and $\left(\begin{matrix}2 \\ 4\end{matrix}\right)$

$\left(\left(1 , 3\right)\right) \times \left(\begin{matrix}- 1 & 2 \\ 2 & 4\end{matrix}\right)$

$\textcolor{w h i t e}{\text{XXX}} = \left(\left(1 \times \left(- 1\right) + 2 \times 2 , 1 \times 2 + 3 \times 4\right)\right)$

$\textcolor{w h i t e}{\text{XXX}} = \left(\left(3 , 14\right)\right)$

Possibility 2
Multiply $\left(\begin{matrix}1 \\ 3\end{matrix}\right)$ by $\left(\left(- 1 , 2 , 2 , 4\right)\right)$
I've left this one undone since I think it is less likely to be what is intended.

Remember:
For matrix multiplication,
$\textcolor{w h i t e}{\text{XXX}}$the number of entries in each row that you are multiplying
$\textcolor{w h i t e}{\text{XXXXXX}}$must be equal to
$\textcolor{w h i t e}{\text{XXX}}$the number of entries in each column that you are multiplying by