# How do you compute the matrix AB given A=((3,0),(-1,5)) and B=((0,4,-1), (-3,3,-5))?

Jan 1, 2017

The answer is $= \left(\begin{matrix}0 & 12 & - 3 \\ - 15 & 11 & - 24\end{matrix}\right)$

#### Explanation:

To compute the matrices, we use the following :

$\left(\begin{matrix}a & b \\ c & d\end{matrix}\right) \left(\begin{matrix}p & q & r \\ s & t & v\end{matrix}\right) = \left(\begin{matrix}a p + b s & a q + b t & a r + b v \\ c p + \mathrm{ds} & c q + t d & c r + \mathrm{dv}\end{matrix}\right)$

Therefore,

$\left(\begin{matrix}3 & 0 \\ - 1 & 5\end{matrix}\right) \left(\begin{matrix}0 & 4 & - 1 \\ - 3 & 3 & - 5\end{matrix}\right) = \left(\begin{matrix}0 & 12 & - 3 \\ - 15 & 11 & - 24\end{matrix}\right)$