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## Homework Statement

I need to prove this:

W, V are linear subspaces

W is a subset of V

-----> dimension(W) ≤ dimension(V)

## Homework Equations

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.

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?