Let U and V be subspaces or Rn. In the case that U V = {0}

Question:

Let U and V be subspaces or Rn. In the case that U ∩ V = {0} we have the following dimension relation
dim (U + V) = dim U + dim V
(See Exercise 18 in Section 4 of Chapter 3.) Make use of the result from Exercise 13 to prove the more general theorem
dim (U + V)= dim U + dim V - dim({/ n V)