1.1. Systems of linear equations
1.2. Row reduction and echelon forms
1.3. Vector equations
1.4. The matrix equation Ax=b
1.5. Solution sets of linear systems
1.7. Linear independence
1.8. Introduction to linear transformations
1.9. The matrix of a linear transformation
1.10 Linear model in business, science, and engineering
2.1. Matrix operations
2.2. The inverse of a matrix
2.3. Characterization of invertible matrices
3.1. Introduction to determinants
3.2. Properties of determinants
3.3. Area and Volume
4.1. Vector spaces and subspaces
4.2. Null spaces, column spaces, and linear transformations
4.3. Linear independent sets; Bases
4.4. Coordinate systems
4.5. The dimension of a vector space
4.6. Rank
5.1. Eigenvectors and Eigenvalues
5.2. The Characteristic Equation
5.3. Diagonalization
6.1. Inner products, length, and orthogonality
6.2. Orthogonal sets
6.3. Orthogonal projections
6.4. The Gram-Schmidt process
6.5. Least square problems