Suppose V is a vector space. Let U, W be subspaces of V. Carefully show that the set U +W= {u+w]u€U, wEW} is a subspace of V. Let S={V1,V2,...,Vk} be a linearly independent set in a vector space V and suppose u Espan (S). Show that there are unique constants C1,C 2..,C k such that u =C¿Vì+C2V 2+...+CkVk.