Vector Subspaces, Span, Linear Combinations - Linear Algebra

This video explains how to test or check if a vector subspace is valid using the definition, theorem, three conditions, properties and axioms. Examples are covered to show the difference between subspace, span or spanning set of two (or more) given vectors u and v, and subset, and how to find it. The meaning and difference between linear combination and linear independent vectors and matrices is deferred to another tutorial.

This linear algebra video covers a tutorial on the subspaces of real vector spaces, linear combinations and span. Several worked examples are covered to reinforce these concepts.

0:00 Vector subspace definition
3:27 Subspaces of common vector spaces
15:01 Subsets that are not vector subspaces
18:41 Linear combinations and span