# How do you find the product of [(1,2), (3,4)][(-1),(3)]?

Dec 19, 2016

The answeris $= \left(\begin{matrix}5 \\ 9\end{matrix}\right)$

#### Explanation:

It's the product of 2 matrices

$\left(\begin{matrix}a & b \\ c & d\end{matrix}\right) \cdot \left(\begin{matrix}e \\ f\end{matrix}\right) = \left(\begin{matrix}a e + b f \\ c e + \mathrm{df}\end{matrix}\right)$

Therefore,

$\left(\begin{matrix}1 & 2 \\ 3 & 4\end{matrix}\right) \cdot \left(\begin{matrix}- 1 \\ 3\end{matrix}\right) = \left(\begin{matrix}- 1 + 6 \\ - 3 + 12\end{matrix}\right)$

$= \left(\begin{matrix}5 \\ 9\end{matrix}\right)$