18.06SC | Fall 2011 | Undergraduate

Linear Algebra

Unit I: Ax = b and the Four Subspaces

Transposes, Permutations, Vector Spaces

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Session Overview

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

To account for row exchanges in Gaussian elimination, we include a permutation matrix P in the factorization PA = LU. Then we learn about vector spaces and subspaces; these are central to linear algebra.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 2.7 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