Topic: Basis and Dimension

Why Too Few Vectors Cannot Span

Why Too Many Vectors Must Be Dependent

Using Exchange to Build a Basis

Unique Coordinates in a Fixed Basis

The Exchange Lemma

The Empty Basis and Lists Containing Zero

The Definition of a Basis

Testing Whether a Vector Lies in a Span

Standard and Nonstandard Bases of Rn

Spans and the Smallest Subspace Containing a Set