| Lecture | Date | Sections from Text | Topics |
| 1 | 6/25 | 1.1, 1.2, 1.3 | Matrices, Vectors, and Systems of Linear Equations |
| 2 | 6/26 | 1.3, 1.4 | Solving systems of linear equations, Gaussian Elimination |
| 3 | 6/27 | 1.6, 1.7 | Span of a set of vectors, Linear dependence and independence |
| 4 | 6/28 | 1.7 | QUIZ; Homogeneous Systems |
| 5 | 7/2 | 2.1, 2.3 | Matrix Algebra, Invertibility |
| 6 | 7/3 | 2.3, 2.4 | Invertibility and elementary matrices, Inverse of a Matrix |
| 7 | 7/5 | 2.5 | QUIZ; LU Decomposition |
| 7 | 7/9 | 3.1, 3.2 | Determinants, Cofactor Expansions, Properties of Determinants |
| 9 | 7/11 | 3.2, 4.1 | More properties of determinants, Subspaces |
| 9 | 7/11 | 4.2, 4.3 | Basis and Dimension, Column Space and Null Space of a Matrix |
| 10 | 7/12 | Review | |
| 12 | 7/16 | Midterm | |
| 12 | 7/17 | 5.1,5.2 | Eigenvalues, Eigenvectors, Characteristic Polynomial |
| 13 | 7/18 | 5.3 | Diagonalization of a Matrix, Examples |
| 14 | 7/19 | 5.5 | QUIZ; Markov Chains |
| 15 | 7/23 | 6.1 | Geometry of Vectors, Orthogonal Projection onto a line |
| 16 | 7/24 | 6.2 | Orthogonal Sets of Vectors, Gram-Schmidt Process |
| 17 | 7/25 | 6.3 | Least Squares; Normal Equations, Orthogonal Projection matrices |
| 18 | 7/26 | 6.4, 6.5 | QUIZ; Orthogonal Matrices, Diagonalization of Symmetric matrices |
| 20 | 7/30 | 6.5 | Spectral Decomposition for Symmetric Matrices, Diagonalization of Quadratic Forms |
| 21 | 7/31 | Review | |
| 22 | 8/1 | Review | |
| 23 | 8/2 | Final Exam | |