I'm having a hard time to prove that two vector sub spaces intersection is the zero space .
I know that I have to prove that they are a direct sum , but I don't really know how to prove that, all I know is the following :
- $F_1, F_2, F_3$ are subspaces
- $F_1 \cap F_2 = (0) $
- $(F_1 + F_2) \cap F_3 = ( 0 )$
I need to prove that : $F_2 \cap F_3 = (0)$ and that $F_1 \cap (F_2 + F_3) = (0)$ , Please don't answer both, just explain how to do the first one and give me a hint to do the second .