# How do you multiply ((1, 2, 12), (13, 2, 1)) with ((4, 8), (4, 3), (5, 2))?

##### 1 Answer
Nov 17, 2016

The answer is $= \left(\begin{matrix}72 & 38 \\ 65 & 112\end{matrix}\right)$

#### Explanation:

The matrix multiplication is

$\left(\begin{matrix}a & b & c \\ d & e & f\end{matrix}\right) . \left(\begin{matrix}l & m \\ n & p \\ q & r\end{matrix}\right)$

$= \left(\begin{matrix}a l + b n + f q & a m + b p + c r \\ \mathrm{dl} + e n + f q & \mathrm{dm} + e p + r f\end{matrix}\right)$

$\left(\begin{matrix}1 & 2 & 12 \\ 13 & 2 & 1\end{matrix}\right) . \left(\begin{matrix}4 & 8 \\ 4 & 3 \\ 5 & 2\end{matrix}\right)$

$= \left(\begin{matrix}4 + 8 + 60 & 8 + 6 + 24 \\ 52 + 8 + 5 & 104 + 6 + 2\end{matrix}\right)$

$= \left(\begin{matrix}72 & 38 \\ 65 & 112\end{matrix}\right)$