# How do you multiply ((2, 1, 2), (0, -1, 3)) and ((4, 7), (-2, -1), (0, 3))?

Mar 4, 2017

See below.

#### Explanation:

I really do wish Socratic had a convenient (or any) drawing tool, as it would make this so much easier.

In summary, here you've got a $2 \times \textcolor{red}{3}$ matrix and a $\textcolor{red}{3} \times 2$ matrix , so you're gonna get a $2 \times 2$ matrix.

You can do this via an elemental summation formula:

${\left(A B\right)}_{i j} = {\sum}_{k} {A}_{i , \textcolor{red}{k}} {B}_{\textcolor{red}{k} , j}$

And so to start, it's 24 + 1 (-2) + 2*(0).....that's just row 1, column 1.

From there, you process the patterns.