18.06SC | Fall 2011 | Undergraduate

Linear Algebra

Unit I: Ax = b and the Four Subspaces

The Four Fundamental Subspaces

« Previous | Next »

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 4th edition or Section 3.5 in the 5th edition.

Problem Solving Video

Check Yourself

Problems and Solutions

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

« Previous | Next »

Course Info

As Taught In
Fall 2011
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