Math 417: Matrix Algebra I
Summer 2022
Embedded Files
Instructor: Wijit Yangjit
Email: yangjit at umich dot edu
Class: TuWeFr 09:00am–10:50am in WH 120
Office Hours: TuWeFr 11:00am–12:00pm in WH 120 or EH Math Common Room
and by appointment
Linear algebra is the study of systems of linear equations: how to solve them and understand properties of their solutions. It is key ingredient in physics, computer science, economics, and many other subjects. In this class, we will cover linear equations, linear transformations, vector spaces, orthogonal transformations, determinants, eigenvalues, eigenvectors, diagonalization, and applications.
Textbook: Linear Algebra with Applications by Otto Bretscher, 5th Edition.
Grading: 30% Homework
30% Midterm Exam
40% Final Exam
Homework
For a problem to receive full credit, you must show all your work, explain your work as necessary, and present your work in a clean and clear format that is easily understood. You may collaborate with other students in solving the homework problems, but you must turn in a write-up in your own words and list your collaborators. You may not post homework problems to internet discussion boards. Homework is due Fridays at 05:00pm in Canvas. No late homework will be accepted under any circumstances, but your lowest homework score will be dropped.
Homework 1 is due on Friday, July 08.
Homework 2 is due on Friday, July 15.
Homework 3 is due on Friday, July 29.
Homework 4 is due on Friday, August 05.
Homework 5 is due on Friday, August 12.
Midterm Exam
The midterm exam is on Friday, July 22, 09:00am–10:50am in WH 120. It covers Chapters 1–3. You are allowed to bring in one 8.5-by-11-inches paper with your notes on it. Calculators are not allowed.
Final Exam
The final exam is on Thursday, August 18, 10:30am–12:30pm in WH 120. It is cumulative. You are allowed to bring in one 8.5-by-11-inches paper with your notes on it. Calculators are not allowed.
Schedule
Wednesday, June 29 Introduction; Gauss–Jordan elimination §1.1 & 1.2
Friday, July 01 The rank of a matrix §1.3
Tuesday, July 05 Introduction to linear transformations and their inverses §2.1
Wednesday, July 06 Linear transformations in geometry §2.2
Friday, July 08 Matrix products §2.3
Tuesday, July 12 Invertibility §2.4
Wednesday, July 13 Image and kernel of a linear transformation §3.1
Friday, July 15 Subspaces of Rn; bases and linear independence §3.2
Tuesday, July 19 The dimension of a subspace of Rn §3.3
Wednesday, July 20 Coordinates §3.4
Friday, July 22 Midterm exam
Tuesday, July 26 Orthogonal projections and orthonormal bases §5.1
Wednesday, July 27 Gram–Schmidt process and QR factorization §5.2
Friday, July 29 Orthogonal transformations and orthogonal matrices §5.3
Tuesday, August 02 Least squares and data fitting §5.4
Wednesday, August 03 Determinants §6.1 & 6.2
Friday, August 05 Geometrical interpretations of the determinant; Cramer's rule §6.3
Tuesday, August 09 Diagonalization §7.1
Wednesday, August 10 Finding the eigenvalues of a matrix §7.2
Friday, August 12 Finding the eigenvectors of a matrix §7.3
Tuesday, August 16 Review
Thursday, August 18 Final exam
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