The Basis of a Subspace

We've seen before the "standard basis vectors" which both span R^n and are linearly independent. However, these aren't the only sets of vectors that have these two properties. We will define such as a set as being a basis for a given subspace.

Learning Objectives:
1) Define a basis.
2) If a set of vectors spans a subspace, decide whether it is a basis
3) Translate between the algebraic notion of solving a system to the geometric notion of linear combination.

This video is part of a Linear Algebra course taught at the University of Cincinnati.

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