The column space of a matrix A tells us when the equation Ax = b will have a solution x. The null space of A tells us which values of x solve the equation Ax = 0.
Lecture Video and Summary
- Watch the video lecture Column Space and Nullspace (00:46:01)
Column Space and Nullspace
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 3.1 through 3.2 in the 4th or 5th edition.
Problem Solving Video
- Watch the recitation video on Vector Subspaces (00:08:45)
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you're done.