1. The problem statement, all variables and given/known data I need to prove this: W, V are linear subspaces W is a subset of V -----> dimension(W) ≤ dimension(V) 2. Relevant equations dimension(X): # of linearly independent vectors in any basis of X 3. The attempt at a solution I'm trying to think this through, but getting stalled. Hmmmm.... Suppose dim(W) > dim(V). Given any basis of W and any basis of V, there will be some vector w* such that w* is contained in the basis of W but not in the basis of V. ..... somehow I'm supposed to deduce a contradiction (if this is even the most efficient way to the conclusion). Help?