For some vectors b the equation Ax = b has solutions and for others it does not. Some vectors x are solutions to the equation Ax = 0 and some are not. To understand these equations we study the column space, nullspace, row space and left nullspace of the matrix A.
Lecture Video and Summary
- Watch the video lecture
The Four Fundamental Subspaces (00:49:20)
The Four Fundamental Subspaces
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 3.6 in the 4th edition or Section 3.5 in the 5th edition.
Problem Solving Video
- Watch the recitation video on
Computing the Four Fundamental Subspaces (00:10:44)
Computing the Four Fundamental Subspaces
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you're done.