# How do you simplify 3[(2,7),(-3,6)]+5[(-6,-4),(3,0)]?

May 26, 2017

$\left[\begin{matrix}- 24 & 1 \\ 6 & 18\end{matrix}\right]$

#### Explanation:

Use this matrix concept: $k \left[\begin{matrix}a & b \\ c & d\end{matrix}\right] = \left[\begin{matrix}k a & k b \\ k c & k d\end{matrix}\right]$

Matrices of the same size/dimension can be added:

$\left[\begin{matrix}a & b \\ c & d\end{matrix}\right] + \left[\begin{matrix}e & f \\ g & h\end{matrix}\right] = \left[\begin{matrix}a + e & b + f \\ c + g & d + h\end{matrix}\right]$

Given: $3 \left[\begin{matrix}2 & 7 \\ - 3 & 6\end{matrix}\right] + 5 \left[\begin{matrix}- 6 & - 4 \\ 3 & 0\end{matrix}\right]$

Multiple by the constants:

$3 \left[\begin{matrix}2 & 7 \\ - 3 & 6\end{matrix}\right] = \left[\begin{matrix}6 & 21 \\ - 9 & 18\end{matrix}\right]$

$5 \left[\begin{matrix}- 6 & - 4 \\ 3 & 0\end{matrix}\right] = \left[\begin{matrix}- 30 & - 20 \\ 15 & 0\end{matrix}\right]$

$\left[\begin{matrix}6 & 21 \\ - 9 & 18\end{matrix}\right] + \left[\begin{matrix}- 30 & - 20 \\ 15 & 0\end{matrix}\right] = \left[\begin{matrix}- 24 & 1 \\ 6 & 18\end{matrix}\right]$