### Lessons

- Lecture 1 – The Geometry of Linear Equations
- Lecture 2 – An Overview of Key Ideas
- Lecture 3 – Elimination with Matrices
- Lecture 4 – Multiplication and Inverse Matrices
- Lecture 5 – Factorization into A = LU
- Lecture 6 – Transposes, Permutations, Vector Spaces
- Lecture 7 – Column Space and Nullspace
- Lecture 8 – Solving Ax = 0: Pivot Variables, Special Solutions
- Lecture 9 – Solving Ax = b: Row Reduced Form R
- Lecture 10 – Independence, Basis and Dimension
- Lecture 11 – The Four Fundamental Subspaces
- Lecture 12 – Matrix Spaces; Rank 1; Small World Graphs
- Lecture 13 – Graphs, Networks, Incidence Matrices
- Unit I: Ax = b and the Four Subspaces – Exam 1 Review
- Unit I: Ax = b and the Four Subspaces – Exam 1