| DATE | LECTURE | TOPICS | READING | HOMEWORK |
| Friday, August 22, 2025 | 1 | Introduction to the course:
Syllabus, etc. Linear equations in linear algebra: Systems of linear equations. |
Lay Section 1.1 | HW
1a Lay Section 1.1: 1, 3, 14, 20, 30, 37. |
| Monday, August 25, 2025 | 2 | Linear equations in linear algebra: Row Reduction and Echelon Form. | Lay
Section 1.2 Here are some slides on the Reduced Row Echelon form of a matrix: Row Reduction |
HW
1b Lay Section 1.2: 1, 2, 7, 16, 41, 42. |
| Wednesday, August 27, 2025 | 3 | Linear equations in linear algebra: Vector equations, span, row span, column span, and the matrix equation Ax = b. | Lay Sections 1.3-4 | HW
1c Lay Section 1.3: 1, 22, 41. Lay Section 1.4: 10, 12, 15. |
| Friday, August 29, 2025 | 4 | Linear equations in linear algebra: Solution sets of linear systems. | Lay
Section 1.5 Here are some slides on solving systems of linear equations with the modified matrix: Modified Matrix |
HW 1 DUE Solution to 1.1.20 1 1 20 Solution to 1.2.7 1 2 7 ____________________ HW 2a Lay Section 1.5: 2, 7, 12, 20, 24, 32. |
| Monday, September 1, 2025 | NO CLASS | LABOR DAY | NO CLASS | |
| Wednesday, September 3, 2025 | 5 | Linear equations in linear algebra: Applications of linear systems, a homogeneous system in economics, balancing chemical equations, network flow. | Lay Section 1.6 | HW
2b Lay Section 1.6: 3, 6, 11. |
| Friday, September 5, 2025 | 6 | Linear equations in linear algebra: Linear independence. | Lay Section 1.7 | HW 2 DUE Solution to 1.5.20 1 5 20 Solution to 1.6.11 1 6 11 ____________________ HW 3a Lay Section 1.7: 2, 6, 22, 24, 26, 28. |
| Monday, September 8, 2025 | 7 | Linear equations in linear algebra: Introduction to linear maps ("transformations" or "mappings"), isomorphisms, and the matrix of a linear transformation. | Lay Sections 1.8-9 | HW
3b Lay Section 1.8: 3, 22, 37. Lay Section 1.9: 2, 14, 38. |
| Wednesday, September 10, 2025 | 8 | Linear equations in linear algebra: Appications: Linear models in business, science, and engineering, constructing nutritious meals, linear equations and electrical networks, difference equations. | Lay Section 1.10 | HW
3c Lay Section 1.10: 1, 10, 11. |
| Friday, September 12, 2025 | 9 | Matrix algebra: Matrix operations, inverse of a matrix, characterizations of invertible matrices. | Lay Sections 2.1-3 | HW 3 DUE Solution to 1.9.2 1 9 2 Solution to 1.9.38 1 9 38 ____________________ HW 4a Lay Section 2.1: 2, 6, 31. Lay Section 2.2: 7, 10, 23. Lay Section 2.3: 4, 12, 35. |
| Monday, September 15, 2025 | 10 | Matrix algebra: Partitioned matrices, matrix factorization, LU factorization. | Lay Sections 2.4-5 | HW
4b Lay Section 2.4: 2, 5, 17. Lay Section 2.5: 1, 24, 25. |
| Wednesday, September 17, 2025 | 11 | Matrix algebra: The Leontief input-output model. | Lay Section 2.6 | HW
4c Lay Section 2.6: 1, 2, 5. |
| Friday, September 19, 2025 | 12 | Matrix Algebra: Applications to computer graphics. | Lay Section 2.7 | HW 4 DUE Solution to 2.2.10 2 2 10 Solution to 2.5.24 2 5 24 ____________________ HW 5a Lay Section 2.7: 2, 3, 4, 13, 19, 20. |
| Monday, September 22, 2025 | 13 | Review | ||
| Wednesday, September 24, 2025 | 14 | Review practice exam | Practice
exam and solutions Sample Midterm1 Sample Midterm1 Sols |
|
| Friday, September 26, 2025 | MIDTERM I | |||
| Monday, September 29, 2025 | 15 | Matrix Algebra: Subspaces of RR^n, column space, kernel ("null space"), basis for a subspace, basis for the kernel, basis for the column space, dimension, rank, rank-nullity theorem ("rank theorem"). | Lay Sections 2.8-9 | HW
5b Lay Section 2.8: 2, 5, 16. Lay Section 2.9: 4, 19, 18. (Number 19 was meant to be number 9.) |
| Wednesday, October 1, 2025 | 16 | Review exam | ||
| Friday, October 3, 2025 | 17 | Determinants: Introduction to determinants, properties of determinants. | Lay Sections 3.1-2 | HW 5 DUE Solution to 2.7.3 2 7 3 Solution to 2.9.4 2 9 4 ____________________ HW 6a Lay Section 3.1: 2, 5, 11. Lay Section 3.2: 2, 7, 28. |
| Monday, October 6, 2025 | 18 | Determinants: Inverse formula, Cramer's Rule, cofactor matrix ("adjugate"), volume, linear maps ("transformations"). | Lay Section 3.3 | HW
6b Lay Section 3.3: 1, 6, 8, 18, 26, 27. |
| Wednesday, October 8, 2025 | 19 | Vector spaces: Vector spaces and subspaces, linear maps ("transformations"), isomorphisms, span, kernel ("null space"), source ("domain"), target ("codomain"), image ("range"), column space, row space. | Lay
Sections 4.1-2 You may also want to take a look at the following pdf: Linear Algebra |
HW
6c Lay Section 4.1: 2, 6, 24. Lay Section 4.2: 2, 8, 26. |
| Friday, October 10, 2025 | 20 | Vector spaces: Linear independence, basis, cooridnate systems, dimension. | Lay Sections 4.3-5 | HW 6 DUE HW 7a Lay Section 4.3: 4, 5. Lay Section 4.4: 2, 10. Lay Section 4.5: 1,9. |
| Monday, October 13, 2025 | 21 | Vector spaces: Change of basis. | Lay Section 4.6 | HW
7b Lay Section 4.6: 1, 2, 5, 8, 11, 16. |
| Wednesday, October 15, 2025 | 22 | Vector spaces: Digital signal processing. | Lay Section 4.7 | HW
7c Lay Section 4.7: 2, 8, 13, 14, 16, 26. |
| Friday, October 17, 2025 | 23 | Vector spaces: Applications to difference equations | Lay Section 4.8 | HW 7 DUE HW 8a Lay Section 4.8: 5, 9, 16, 17, 28, 31. |
| Monday, October 20, 2025 | 24 | Eigenvectors and eigenvalues: Introduction to eigenvectors and eigenvalues. | Lay Section 5.1 | HW
8b Lay Section 5.1: 2, 7, 22, 24, 35, 37. |
| Wednesday, October 22, 2025 | 25 | Eigenvectors and eigenvalues: Characteristic polynomial and equation. | Lay Section 5.2 | HW
8c Lay Section 5.2: 1, 9, 15, 22, 24, 32. |
| Friday, October 24, 2025 | 26 | Eigenvalues and eigenvectors: Diagonalization. | Lay Section 5.3 | HW 8 DUE HW 9a Lay Section 5.3: 1, 5, 22, 30, 33, 37. |
| Monday, October 27, 2025 | 27 | Review | ||
| Wednesday, October 29, 2025 | 28 | Review practice exam | Practice exam and solutions | |
| Friday, October 31, 2025 | MIDTERM II | |||
| Monday, November 3, 2025 | 29 | Eigenvectors and eigenvalues: Eigenvalues and linear maps ("transformations"). | Lay Section 5.4 | HW
9b Lay Section 5.4: 2, 6, 10, 15, 27, 28. |
| Wednesday, November 5, 2025 | 30 | Review exam | ||
| Friday, November 7, 2025 | 31 | Eigenvalues and eigen vectors: Complex eigenvalues. | Lay Section 5.5 | HW 9 DUE HW 10a Lay Section 5.5: 1, 2, 8, 14, 27, 28 (Exercise 28 is FALSE as stated -- see if you can find the error -- the solution, when posted, will explain the error). |
| Monday, November 10, 2025 | 32 | Eigenvalues and eigen vectors: Discrete dynamical systems. | Lay Section 5.6 | HW
10b Lay Section 5.6: 1, 2, 6, 8, 12, 18. |
| Wednesday, November 12, 2025 | 33 | Eigenvalues and eigen vectors: Applications to differential equations. | Lay Section 5.7 | HW
10c Lay Section 5.7: 1, 2, 4, 7, 9, 10. |
| Friday, November 14, 2025 | 34 | Eigenvalues and eigen vectors: Applications to Markov chains. | Lay Section 5.9 | HW 10 DUE HW 11a Lay Section 5.9: 1, 2, 6, 10, 15, 16. |
| Monday, November 17, 2025 | 35 | Orthogonality and least squares: Inner product, dot product, length, orthogonality, orthogonal sets, orthogonal projection. | Lay Sections 6.1-2 | HW
11b Lay Section 6.1: 20,30, 38. Lay Section 6.2: 3, 11, 34. |
| Wednesday, November 19, 2025 | 36 | Orthogonality and least squares: Orthgonal projection, Gram-Schmidt. | Lay Sections 6.3-4 | HW
11c Lay Section 6.3: 1, 12, 22. Lay Section 6.4: 4, 10, 23. |
| Friday, November 21, 2025 | 37 | Orthogonality and least squares: Least squares problems. | Lay Section 6.5 | HW 11 DUE HW 12a Lay Section 6.5: 2, 6, 12, 27, 28, 30. |
| Monday, November 24, 2025 | NO CLASS | THANKSGIVING BREAK | NO CLASS | |
| Wednesday, November 26, 2025 | NO CLASS | THANKSGIVING BREAK | NO CLASS | |
| Friday, November 28, 2025 | NO CLASS | THANKSGIVING BREAK | NO CLASS | |
| Monday, December 1, 2025 | 38 | Orthogonality and least squares: Machine learning and linear models. | Lay Section 6.6 | HW
12b Lay Section 6.6: 1, 2, 5, 13a, 20, 25. |
| Wednesday, December 3, 2025 | 39 | Review | ||
| Friday, December 5, 2025 | 40 | Review practice exam | HW 12 DUE | |
| Tuesday, December 9, 2025 | FINAL EXAM Tuesday, December 9, 2025, 1:30 PM -- 4:00 PM MEUN E064 (Lecture Room) | EXAM SCHEDULE | ||