Theorems about bases of subspaces

All of them come around to the same thing:

• If you have a set of basis vectors.

• And there an $k$ vectors in the set.

• Then any other set of basis vectors, must have $n$ elements.

• If you have less than $n$, then your set cannot span the subspace.

• If you have more than $n$, then your set is linearly dependent.