# How do you multiply ((1, -3, 2), (2, 1, -3), (4, -3, -1)) and ((1, 4, 1, 0), (2, 1, 1, 1), (1, -2, 1, 2))?

May 30, 2016

$\left(\begin{matrix}- 3 & - 3 & 0 & 1 \\ 1 & 15 & 0 & - 5 \\ - 1 & 11 & 2 & - 1\end{matrix}\right)$

#### Explanation:

Matrices could be multiplied only if first one has as many columns as the second one has rows. In that case it's true - first has 3 columns and second has 3 rows, so we can multiply.
The result will have as many rows as first matrix and as many columns as second matrix.
Everything will be clear from following instruction:

• Lift the second matrix to make room for result.
• To obtain any element take a row directly to the left of it and a column directly above it (for the first element it is $\left(\left(1 , - 3 , 2\right)\right)$ and $\left(\begin{matrix}1 \\ 2 \\ 1\end{matrix}\right)$)
• multiply them pairwise and take sum: $1 \cdot 1 + \left(- 3\right) \cdot 2 + 2 \cdot 1 = 1 - 6 + 2 = - 3$
• the number you get is this element of resulting matrix

Here is the whole thing:

$\textcolor{w h i t e}{- - - - - - 0} \left(\begin{matrix}1 & 4 & 1 & 0 \\ 2 & 1 & 1 & 1 \\ 1 & - 2 & 1 & 2\end{matrix}\right)$
$\left(\begin{matrix}1 & - 3 & 2 \\ 2 & 1 & - 3 \\ 4 & - 3 & 1\end{matrix}\right) \left(\begin{matrix}- 3 & - 3 & 0 & 1 \\ 1 & 15 & 0 & - 5 \\ - 1 & 11 & 2 & - 1\end{matrix}\right)$

For other multiplying examples:
How do I do multiplication of matrices?
use wolfram alpha