If $\begin{bmatrix} a + b & a - 2c \\ 2a - b & c + d \end{bmatrix} = \begin{bmatrix} 4 & 1 \\ 11 & 9 \end{bmatrix}$, what is $a + b + c + d$?

Explanation

1. 01

   From the first column: $a + b = 4$ and $2a - b = 11$. Adding, $3a = 15$, so $a = 5$ and $b = -1$.

2. 02

   Then $a - 2c = 1$ gives $c = 2$, and $c + d = 9$ gives $d = 7$.

3. 03

   So $a + b + c + d = 13$.