Video shows an example of proving a particular linear combination of 3 vectors in R3 spans R3. Relates this to linearly independent and linearly dependent vectors. [16:53]

Video defines a vector subspace by its three criteria: containing the zero vector, closure under scalar multiplication and closure under vector addition. Gives examples of vector sets and testing to see if they are vector subspaces. Then...

Introduction to linear subspaces. This video gives examples of vector sets and testing to see if they are vector subspaces.

Video explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors. Shows a proof that two non-parallel...