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..