Hey, I am confused about this question. I need some help getting started.

Let $\displaystyle V= \sum U_k$ where $\displaystyle V$ is a vector space and $\displaystyle U_1,...,U_j$ are the subspaces of $\displaystyle V$.

Use the fact that $\displaystyle U_1 \cap U_2 =0,..., (U_1+...+U_{j-1}) \cap U_j=0$ to prove that $\displaystyle V$ is the direct sum of the subspaces $\displaystyle U_1,...,U_j$.

Where should I start with this? Thanks for any help.