18.06SC | Fall 2011 | Undergraduate

Linear Algebra

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

As Taught In
Fall 2011
Learning Resource Types
Lecture Videos
Exams with Solutions
Lecture Notes
Recitation Videos
Problem Sets with Solutions
Course Introduction
Instructor Insights