Unit I: Ax = b and the Four Subspaces

The Geometry of Linear Equations

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Session Overview

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

A major application of linear algebra is to solving systems of linear equations. This lecture presents three ways of thinking about these systems. The “row method” focuses on the individual equations, the “column method” focuses on combining the columns, and the “matrix method” is an even more compact and powerful way of describing systems of linear equations.

Portion of Fig. 2.2 from the textbook Introduction to Linear Algebra.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 1.1, 1.2, and 2.1 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