Basis Vectors and Coordinates

This video is about sets of vectors that define a basis for a subspace, as well as how to find coordinates relative to a particular basis. Finding the basis of the null space and column space of a matrix are addressed in detail. Table of contents below.

00:00 - Introduction
00:24 - Definition of basis
00:36 - Example
02:28 - Example of defining a vector in terms of different bases
06:37 - Coordinates in terms of any basis
07:55 - Another example
09:57 - Finding a basis for the null space of a matrix
13:06 - Finding general coordinates relative to a basis
13:39 - Finding a basis for the column space of a matrix
21:33 - Conclusion