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
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Column Space and Nullspace (00:46:01)
Column Space and Nullspace
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- Lecture video transcript (PDF)
- Read Section 3.1 through 3.2 in the 4th or 5th edition.
Problem Solving Video
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Vector Subspaces (00:08:45)
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Problems and Solutions
Work the problems on your own and check your answers when you're done.