The Four Fundamental Subspaces

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

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.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 3.6 in the textbook.

Problem Solving Video

  • Watch the recitation video on Computing the Four Fundamental Subspaces (00:10:44)
  • Recitation video transcript (PDF)

Check Yourself

Problems and Solutions

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


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