If $A' = \begin{bmatrix}3 & -1 \\ 2 & 4\end{bmatrix}$ and $B = \begin{bmatrix}1 & 0 \\ -2 & 5\end{bmatrix}$, what is $(A + 2B)'$?

Explanation

1. 01

   $(A + 2B)' = A' + 2B'$, and $A'$ is given.

2. 02

   $B' = \begin{bmatrix}1 & -2 \\ 0 & 5\end{bmatrix}$, so $A' + 2B' = \begin{bmatrix}3 & -1 \\ 2 & 4\end{bmatrix} + \begin{bmatrix}2 & -4 \\ 0 & 10\end{bmatrix} = \begin{bmatrix}5 & -5 \\ 2 & 14\end{bmatrix}$.