Linear algebra and applications: video 6 Matrix spaces part 1

Matrix spaces: part 1

Vector spaces and subspaces:
Introduction: 00:00
Subspaces of vectors: 00:48
Column space of A: 03:21
Null space of A: 10:02
Example 1: 12:39
Example 2: 14:52
Example 3: 17:42
Echelon matrix: 25:42
Row reduced echelon matrix: 27:29
Rank and row reduced form:
Rank: 29:38
Rank: application to Example 3: 29:54
Rank 1 matrices: 30:29
Pivot columns: 33:18
Special solutions: 38:27
Application to Example 3: 41:09
Complete solution to Ax=b:
Particular solution: 44:58
Methodology: 46:58
Example: 50:25
Whiteboard exercise: 53:49