If $\begin{bmatrix} a + b & a - 2c \\ 2a - b & c + d \end{bmatrix} = \begin{bmatrix} 7 & 0 \\ -1 & 5 \end{bmatrix}$, what is $a + b + c + d$?

Explanation

1. 01

   From the first column: $a + b = 7$ and $2a - b = -1$. Adding, $3a = 6$, so $a = 2$ and $b = 5$.

2. 02

   Then $a - 2c = 0$ gives $c = 1$, and $c + d = 5$ gives $d = 4$.

3. 03

   So $a + b + c + d = 12$.