| Lecture | Date | Section | Topic | Homework |
|---|---|---|---|---|
| 1 | 1/15 | No class | ||
| 2 | 1/17 | No class | ||
| 3 | 1/20 | 1.1 | Systems of Linear Equations | 1.1# 1, 2, 3, 7, 8, 13, 18 |
| 4 | 1/22 | 1.2 | Row Reduction and Echelon Forms | 1.2# 1, 2, 3, 4, 7, 10, 13, 14, 21 |
| 5 | 1/24 | 1.3 | Vector Geometry (video 1, video 2) | 1.3# 1, 2, 3, 4 and the in-class problems |
| 6 | 1/27 | 1.3 | Vector Equations (video) | 1.3# 9, 10, 11, 13, 28 |
| 7 | 1/29 | 1.4 | The Matrix Equation Ax = b | 1.4# 1-4, 6, 8, 10, 11, 13, 17-20 |
| 8 | 1/31 | 1.5 | Solution Sets of Linear Systems | 1.5# 5, 11, 12, 14, 15, 17, 34 |
| 9 | 2/03 | 1.7 | Linear Independence | 1.7# 2, 4, 7, 8, 10, 20, 27, 28, 40 |
| 10 | 2/05 | 1.8 | Introduction to Linear Transformations | 1.8# 4, 8, 9, 13, 17, 18, 29, 32 |
| 11 | 2/07 | 1.9 | The Matrix of a Linear Transformation | 1.9# 1, 3, 17, 31, 32, 37 |
| 12 | 2/10 | 2.1 | Matrix Operations | 2.1# 1, 2, 3, 11, 27 |
| 13 | 2/12 | Midterm 1 | ||
| 14 | 2/14 | 2.2 | The Inverse of a Matrix | 2.2# 3, 6, 8, 16, 33 |
| 15 | 2/17 | 2.3 | Characterizations of Invertible Matrices | 2.3# 6, 8, 15, 16, 34 |
| 16 | 2/19 | 2.8 | Subspaces of R^n | 2.8# 1, 2, 6, 7, 12, 19, 20 |
| 17 | 2/21 | 2.9 | Dimension and Rank | 2.9# 9, 10, 14, 15, 19, 20, 22, 24 |
| 18 | 2/24 | 3.1 | Introduction to Determinants | 3.1# 9, 13, 16, 20, 22 |
| 19 | 2/26 | 3.2 | Properties of Determinants | 3.2# 5, 15-18, 22, 26, 29, 36 |
| 20 | 2/28 | 3.3 | Cramer's Rule, Volume, and Linear Transformations | 3.3# 7, 8, 19, 20, 21, 28, 30 |
| 21 | 3/03 | 4.1 | Abstract Vector Spaces | |
| 22 | 3/05 | 5.1 | Eigenvectors and Eigenvalues | 5.1# 2, 4, 7, 17, 18, 19, 35, 37 |
| 23 | 3/07 | 5.2 | The Characteristic Equation | 5.2# 2, 4, 9, 12, 16, 19 |
| 24 | 3/17 | 5.3 | Diagonalization | 5.3# 1, 2, 5, 12, 15 |
| 25 | 3/19 | Review | ||
| 26 | 3/21 | Midterm 2 | ||
| 27 | 3/24 | 5.4 | Eigenvectors and Linear Transformations | 4.4# 3, 5, 11; 5.4# 12, 14, 17, 30 |
| 28 | 3/26 | 5.5 | Complex Eigenvalues | 5.5# 1, 4, 6, 7, 10 |
| 29 | 3/28 | 5.6 | Discrete Dynamical Systems | 5.6# 1, 3, 4, 5, 17, 18 |
| 30 | 3/31 | 5.7 | Applications to Differential Equations | 5.7# 1, 2 |
| 31 | 4/02 | 6.1 | Dot Products and Orthogonality | 6.1# 1, 4, 6, 8, 9, 14, 15-18, 27 |
| 32 | 4/04 | 6.1 | Fundamental Theorem of Linear Algebra | These problems |
| 33 | 4/07 | 6.2 | Orthogonal Sets | 6.2# 2, 4, 6, 7, 10, 12, 13, 35 |
| 34 | 4/09 | 6.3 | Orthogonal Projections | 6.3# 2, 4, 10, 11, 25, 26 |
| 35 | 4/11 | 6.5 | Least-Squares Problems | 6.5# 3, 5, 7, 25 |
| 36 | 4/14 | 6.6 | Applications to Regression | 6.6# 7, 11 |
| 37 | 4/16 | Midterm 3 | ||
| 38 | 4/18 | 6.4 | The Gram-Schmidt Process | 6.4# 2, 3, 4, 7, 8, 25 |
| 39 | 4/21 | 7.1 | Symmetric Matrices | 7.1# 27, 28, 29, 35, 36 (Hint: Prove that Bz=0) |
| 40 | 4/23 | 7.2 | Quadratic Forms | 7.1# 17; 7.2# 3, 7, 9 |
| 41 | 4/25 | 7.4 | The Singular Value Decomposition | |
| 42 | 4/28 | 7.5 | Applications of the SVD |