I'm having a very difficult time understanding a basis. I understand that it's basically just coordinates that span a subspace, but can someone help me to understand how a set can span a subspace and be a linearly independent set?
If a set spans a subspace doesn't this mean that any vector can be represented by a linear combination of the vectors in the subspace? If that is the case, isn't this a direct contradiction to the set being linearly independent?
What am I missing here?