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Session Overview

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.

Session Activities

Lecture Video and Summary

• Watch the video lecture Column Space and Nullspace
• Read the accompanying lecture summary (PDF)
• Lecture video transcript (PDF)

Suggested Reading

• Read Section 3.1 through 3.2 in the 4^th or 5^th edition.

Problem Solving Video

• Watch the recitation video on Vector Subspaces
• Recitation video transcript (PDF)

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you’re done.

• Problems (PDF)
• Solutions (PDF)

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