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Back to the class
Course definition: Systems of linear equations, matrices, vector spaces, inner products, linear transformations, determinants, and eigenvalues. (from here)

Chapter 1
- Section 1-Systems of Linear Equations
- Section 2-Row Reduction and Echelon Forms
- Section 3-Vector Equations
- Section 4-The Matrix Equation $Ax=\textbf{b}$
- Section 5-Solution Sets of Linear Systems
- ~~Section 6-Applications of Linear Systems~~
- Section 7-Linear Independence
- Section 8-Introduction to Linear Transformations
- Section 9-The Matrix of a Linear Transformation
- ~~Section 10-Linear Models in Business, Science, and Engineering~~
Chapter 2
- Section 1-Matrix Operations
- Section 2-The Inverse of a Matrix
- Section 3-Characterizations of Invertible Matrices
- Section 4-Partitioned Matrices
- Section 5-Matrix Factorizations
- ~~Section 6-The Leontief Input-Output Model~~
- ~~Section 7-Applications to Computer Graphics~~
- ~~Section 8-Subspaces of $\mathbb{R}^n$~~
- ~~Section 9-Dimension and Rank~~
Chapter 3
- Section 1-Introduction to Determinants
- Section 2-Properties of Determinants
- Section 3-Cramer's Rule, Volume, and Linear Transformations
Chapter 4
- Section 1-Vector Spaces and Subspaces
- Section 2-Null Spaces,Column Spaces, and Linear Transformations
- Section 3-Linear Independent Sets; Bases
- Section 4-Coordinate Systems
- Section 5-The Dimension of a Vector Space
- Section 6-Rank
- Section 7-Change of Basis
- ~~Section 8-Applications to Difference Equations~~
- ~~Section 9-Applications to Markov Chains~~
Chapter 5
- Section 1-Eigenvectors and Eigenvalues
- Section 2-The Characteristic Equation
- Section 3-Diagonalization
- Section 4-Eigenvectors and Linear Transformations
- Section 5-Complex Eigenvalues
- ~~Section 6-Discrete Dynamical Systems~~
- ~~Section 7-Applications to Differential Equations~~
- ~~Section 8-Iterative Estimates for Eigenvalues~~
Chapter 6

Section 1-Inner Product, Length, and Orthogonality
Section 2-Orthogonal Sets
Section 3-Orthogonal Projections
Section 4-The Gram-Schmidt Process
Section 5-Least-Squares Problems
~~Section 6-Applications to Linear Models~~
~~Section 7-Inner Product Spaces~~
Section 8-Applications of Inner Product Spaces