Let $W$ be a vector subspace of $F_2^n$. Then, $|W| = 2^k$ for $k \leq n$. Is it always true that $\text{dim}(W) = k$? If it is, where can I find a proof?
Dimension of a vector subspace of $F_2^n$
1
$\begingroup$
linear-algebra
-
9It may be easier to go the other way. If $W$ has a basis consisting $k$ vectors, how many elements does it have? Try it this way, if you are stuck! – 2011-08-31