Please help with algrebra proof Let V be a finite dimensiona

Please help with algrebra proof.

Let V be a finite dimensional vector space. Suppose U and W are subspaces of V. Prove that the sum U+W is a direct sum if and only if dim(U+W)=dim(U)+dim(W).

Thank you

Solution

Let U and W be sunspaces of V. then V0U+W if and only if for every v belongs V there exist unique vector u that belongs to U and w belongs to W such that v=u+w.