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 Notes	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 Notes	HW 1 DUE 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 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 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 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
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.
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 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, 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"), image, column space, row space.	Lay Sections 4.1-2 You may also want to take a look at the following pdf: Linear Algebra Notes	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