An old exam I'm practicing with asks: $$ W_1 = \left \{ \begin{bmatrix}a & a\\0 & b\end{bmatrix}: a,b \in R \right\} \ and \ W_2 = \left \{ \begin{bmatrix}c & d\\c & 0\end{bmatrix}: c,d \in R \right\}$$
Find a basis of $ W_1 + W_2$ and of $W_1 \bigcap W_2$.
How do I add two 'spaces' together? Can I simply say that $W_1 + W_2$ is equal to $$\left \{ \begin{bmatrix}a+c & a+d\\c & b\end{bmatrix}: a,b,c,d \in R \right\}$$ It just seems too easy!