Unit I: Ax = b and the Four Subspaces

Solving Ax = 0: Pivot Variables, Special Solutions

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Session Overview

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

We apply the method of elimination to all matrices, invertible or not. Counting the pivots gives us the rank of the matrix. Further simplifying the matrix puts it in reduced row echelon form R and improves our description of the null space.

Session Activities

Lecture Video and Summary

Suggested Reading

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

Problem Solving Video

Check Yourself

Problems and Solutions

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

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Course Info

Learning Resource Types

theaters Lecture Videos
grading Exams with Solutions
notes Lecture Notes
theaters Recitation Videos
assignment_turned_in Problem Sets with Solutions
laptop_windows Simulations
groups Course Introduction
co_present Instructor Insights