We'd like to be able to "invert A" to solve Ax = b, but A may have only a left inverse or right inverse (or no inverse). This discussion of how and when matrices have inverses improves our understanding of the four fundamental subspaces and of many other key topics in the course.
Note: In the Fall of 1999, when the lecture videos were recorded, this lecture was given after exam 3. For the OCW Scholar version of the course we have moved it into the main body of material.
Lecture Video and Summary
- Watch the video lecture Left and Right Inverses; Pseudoinverse (00:41:53)
Lecture 33: Left and Right Inverses; Pseudoinverse
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 7.3 in the 4th edition or Section 8.3 in the 5th edition.
Problem Solving Video
- Watch the recitation video on Pseudoinverses (00:14:39)
Problem Solving: Pseudoinverses
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you're done.