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.
Lecture Video and Summary
- Watch the video lecture Transposes, Permutations, Vector Spaces (00:47:42)
Transposes, Permutations, Vector Spaces
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 2.7 in the 4th or 5th edition.
Problem Solving Video
- Watch the recitation video on Subspaces of Three Dimensional Space (00:14:44)
Subspaces of Three Dimensional Space
- Recitation video transcript (PDF)
- 观看视频: 习题讲解 -- 三维空间的子空间 (00:13:07)
Problems and Solutions
Work the problems on your own and check your answers when you're done.