I need to prove this:
W, V are linear subspaces
W is a subset of V
-----> dimension(W) ≤ dimension(V)
dimension(X): # of linearly independent vectors in any basis of X
The Attempt at a Solution
I'm trying to think this through, but getting stalled.
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).