Unit I: Ax = b and the Four Subspaces

Transposes, Permutations, Vector Spaces

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Session Overview

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

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