Transposes, Permutations, Vector Spaces
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
- Watch the video lecture Transposes, Permutations, Vector Spaces (00:47:42)
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
Suggested Reading
- Read Section 2.7 in the textbook.
Problem Solving Video
- Watch the recitation video on Subspaces of Three Dimensional Space (00:14:44)
- Recitation video transcript (PDF)
Check Yourself
Problems and Solutions
Work the problems on your own and check your answers when you're done.
