In R4, let U be the subspace of all vectors of the form (u1, u2, 0, 0)T,

Question:

In R4, let U be the subspace of all vectors of the form (u1, u2, 0, 0)T, and let V the subspace of all vectors of the form (0, v2, v3, 0)T. What are the dimensions of U, V, U ∩ V, U + V? Find a basis for each of these four subspaces. (See Exercises 18 and 20 of Section 2.)