| Lecture | Date | Section Covered |
| 1 | 1.1, 1.2 Matrices and Vectors | |
| 2 | 1.3 Systems of Linear Equations | |
| 3 | 1.4 Gaussian Elimination | |
| 4 | 1.6 Span of a Set of Vectors | |
| 5 | 1.7 Linear Dependence and Linear Independence | |
| 6 | 1.7, 2.1 Homogeneous Systems, Matrix Multiplication | |
| 7 | 2.1 Matrix Algebra; Quiz 1 | |
| 8 | 2.3, App.E Invertibility and Elementary Matrices, Uniqueness of RREF | |
| 9 | 2.4, 2.5 Inverse of a Matrix, Partitioned Matrices and Block Multiplication | |
| 10 | 2.6 LU Decomposition of a Matrix; Review for the exam | |
| 11 | Oct 8 | Midterm Exam 1 |
| 12 | 3.1 Determinants; Cofactor Expansions | |
| 13 | 3.2 Properties of Determinants | |
| 14 | 4.1 Subspaces | |
| 15 | 4.2 Basis and Dimension | |
| 16 | 4.3 Column Space and Null Space of a Matrix | |
| 17 | 5.1 Eigenvalues and Eigenvectors; Quiz 2 | |
| 18 | 5.2 Characteristic Polynomial | |
| 19 | 5.3 Diagonalization of a Matrix | |
| 20 | 5.5 Applications of Eigenvalues; Review for the exam | |
| 21 | 11/12 | Midterm Exam 2 |
| 22 | 6.1 Geometry of Vectors; Projection onto a Line | |
| 23 | 6.2 Orthogonal Sets of Vectors; Gram - Schmidt Process; QR factorization | |
| 24 | 6.3 Orthogonal Projection; Othogonal Complements | |
| 25 | 6.4 Least Squares; Normal Equations; Quiz 3 | |
| 26 | 6.5, 6.6 Orthogonal Matrices; Diagonalization of Symmetric Matrices | |
| 27 | 6.6 Spectral Decomposition for Symmetric Matrices, Diagonalization of Quadratic Forms | |
| 28 | Review for the Final Exam |