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

May 24, 2018

#### Explanation:

Matrix multiplication is

$\left(\begin{matrix}a & b \\ c & d \\ e & f\end{matrix}\right) \times \left(\begin{matrix}p & q \\ r & s\end{matrix}\right) = \left(\begin{matrix}\text{ap+br" & "aq+bs" \\ "cp+dr" & "cq+ds" \\ "ep+fr" & "eq+fs}\end{matrix}\right)$

Therefore, the matrix multiplications are

$\left(\begin{matrix}3 & - 2 \\ 3 & 1 \\ - 2 & 4\end{matrix}\right) \times \left(\begin{matrix}3 & 1 \\ - 2 & 4\end{matrix}\right) = \left(\begin{matrix}13 & - 5 \\ 7 & 7 \\ - 14 & 14\end{matrix}\right)$

$\left(\begin{matrix}3 & - 2 \\ 3 & 1 \\ - 2 & 4\end{matrix}\right) \times \left(\begin{matrix}- 2 & 4 \\ 1 & 3\end{matrix}\right) = \left(\begin{matrix}- 8 & 6 \\ - 7 & 15 \\ 8 & 4\end{matrix}\right)$