Clayton Shonkwiler

Math 369

Instructor: Dr. Clayton Shonkwiler
Time: Monday, Wednesday, Friday 8:00–8:50
Location: Engineering E105
Office: Weber 216
Office Hours: Tuesday 1:00–2:00, Wednesday 1:00–2:00 and 3:00–4:00, Thursday 2:00–3:00
Text: Elementary Linear Algebra, by Howard Anton
Email Address:




Practice Problems for Exam 1 (solutions)
Practice Problems for Exam 2 (solutions)
Practice Problems for Exam 3 (solutions)
Practice Problems for Final Exam (solutions)

Summary of the Course

Linear algebra is one of the most important and fundamental subjects in mathematics: virtually every area of mathematics relies on or extends the tools of linear algebra. Moreover, linear algebra provides the theoretical underpinnings for countless applications in scientific computation, engineering, and statistical models in the social sciences.

This course provides an introduction to the ideas and methods of linear algebra, which you will learn by understanding them geometrically, justifying them algebraically, and using them to solve problems in various disciplines. In addition, the course serves as an introduction to abstract reasoning and mathematical proof. It is a prerequisite for all advanced courses in mathematics and provides excellent preparation for graduate work in the natural sciences and quantitative social sciences.


Homework will be collected approximately weekly. Each assignment will consist of a reading assignment and a number of problems to be done. Assignments will be posted to the course webpage as well as to Canvas.

Homework is an important part of any math class, as it is impossible to learn mathematics without actually doing mathematics. The goal of the assignments is to deepen your understanding of the concepts, tools and techniques discussed in class, as well as to give you the opportunity to practice explaining your mathematical thinking. The importance of effective communication is vital: knowledge without the ability to communicate that knowledge is of limited value. As such, to get full credit on a problem your solution must be clear and well-written.

Homework must be stapled with your name clearly written at the top. What you turn in should be a final copy: it should be neat, legible, and well-organized. If I can’t read or understand your work you won’t receive any credit.

Late homework will not be accepted, so you should turn in whatever you have completed on the due date in order to get credit for it. There will be no exceptions to this: as explained in the section on grading below, not turning in homework will not hurt your grade (except insofar as it hurts your understanding of the material).

I strongly encourage you to work on solving homework problems with your fellow classmates. However, the work you turn in must reflect your own knowledge and understanding and not that of anyone else. Therefore, you must write up your solutions by yourself.


There will be three midterm exams and a final. The midterms will be 50 minute in-class exams and are tentatively scheduled for February 17, March 31, and April 28. The final exam will occur in Engineering E105 (our regular classroom) from 11:50–1:50 on Wednesday, May 10.

No make-up examinations will be given in the course. If you are absent from a scheduled exam and your absence is excused (with supporting documentation from, e.g., a medical or legal professional), the portion of the course grade determined by the missing exam will be divided equally between the other exams (including the final). Please let me know as soon as possible if you have a conflict with one of the test dates.


Your final grade in the course will be determined by:

Homework and Class Participation: 25% (see below)

Exams: 15% each

Final Exam (comprehensive): 30%

Here’s how the grading process works. First, I compute an overall course grade for you on a scale of 0–100 by combining your exam and homework grades using the weights above. For example, if you have scores of 75%, 80%, and 85% on the three midterms, 85% on the final, and 90% on the homework and class participation, I would compute this score as \[\underbrace{0.75\times 15+0.80\times 15 + 0.85\times 15}_{\text{midterm exams}}\ +\ \underbrace{0.85 \times 30}_{\text{final}}\ +\ \underbrace{0.90\times 25}_{\text{homework}} = 84.\]

Next, I divide by the sum of the exam weights (\(15+15+15+30=75\)) plus the fraction of points earned on homework (in the example, \(0.90 \times 25 = 22.5\)), so the final score in this case would be \[\frac{84}{75+22.5} = \frac{84}{97.5} \approx 0.862.\]

In other words, after reweighting, your final score in the class is given by \[\frac{\text{points earned on homework} + \text{points earned on exams}}{\text{points earned on homework} + \text{points available on exams}}.\] This means, in particular, that homework cannot possibly hurt your final grade and, since homework points are usually easier to earn than exam points, the more homework you do, the better your final grade will be.

Finally, after computing the above score score, I rank everybody in the class in order by their score and assign cutoffs for ‘A’, ‘B’, ‘C’, and ‘D’. Generally these are somewhat lower than the traditional 90, 80, 70, and 60. When setting the cutoff I consider the students immediately above and below the line and try to take into account improvement and other circumstances. That being said, the list is never, ever reordered. Regardless of other circumstances, a better score in the class should always earn at least as good a letter grade. Ultimately, I can only grade the course based on what’s in your written work.

Scores will be maintained on Canvas; please check occasionally to make sure your scores have been entered correctly.


You are expected to attend class every day, to participate in class, to read the textbook, and to do the homework.

Academic Integrity

As a Colorado State University student, you have agreed to abide by the University Policy on Academic Integrity and by the Student Conduct Code. Please see for more on academic integrity at CSU. All academic work must meet the standards described in the Academic Integrity Policy. At a minimum, violations will result in a grading penalty in this course and a report to the Office of Conflict Resolution and Student Conduct Services.

Lack of knowledge of the academic honesty policy is not a viable explanation for a violation. Questions related to coursework and the academic integrity policy should be discussed with the instructor.

You are encouraged to discuss homework problems with your classmates, but the work you turn in must be your own, and in particular you should write up your final solutions independently. Remember that for all work in this course, the CSU honor pledge applies: “I have not given, received, or used any unauthorized assistance.”

Additional help

If I were a perfect teacher, you could learn everything you need to know just by going to class and doing the assignments. Unfortunately, I am not a perfect teacher, so there’s a good chance that, at some point, you’ll find yourself confused, stuck or otherwise frustrated by the material or the course. If you do, ask for help! Office hours are, of course, an excellent venue for this, but if you feel uncomfortable asking my help or if you find that my teaching style and your learning style simply don’t mesh, there are many other resources available to you.

First and foremost, your fellow classmates are a great resource. Odds are that, for any question you have, there’s someone in the class who can answer it, so don’t be afraid to ask. Even the simple process of explaining why you’re stuck to someone who is just as confused as you is often enough to make things clearer. Just be sure to return the favor when you get the chance to help someone else.

Second, TILT provides math and science tutoring every Sunday–Thursday from 5:00–10:00 PM. The Tutoring@CSU site is also a good resource; for example, it also maintains a list of private tutors.

Third, the math department maintains its own list of recommended private tutors (typically graduate students).

If none of the above is suitable or practical, please let me know and I’ll be happy to help you find additional resources.


If you think you may need accommodations in this course due to the impact of a disability please meet with me privately during the first week of class. You should also contact the Resources for Disabled Students office to confirm your eligibility for appropriate accommodations. Doing so early in the semester will help prevent unnecessary inconvenience.

All of the course materials, including tests and exams, are copyright by the instructor, even if the © symbol does not appear on them. You may not upload or post copies of these materials to the web without explicit written permission.


The course syllabus is a general plan for the course; deviations announced in class may be necessary.

Anticipated Schedule

Week Subjects (Sections from the text)
01.17–01.20 Systems of linear equations (§1.1–1.2)
01.23–01.27 Matrix operations and inverses (§1.3–1.5)
01.30–02.03 Special Matrices and transformations (§1.6–1.9)
02.06–02.10 Determinants (§2.1–2.3)
02.13–02.17 Euclidean Vector Spaces (§3.1) MIDTERM #1
02.20–02.24 Geometry of vector spaces (§3.2–3.5)
02.27–03.03 Abstract vector spaces and subspaces (§4.1–4.2)
03.06–03.10 Linear independence and bases (§4.3–4.5)
03.13–03.17 SPRING BREAK
03.20–03.24 Change of basis and special subspaces (§4.6–4.8)
03.27–03.31 Matrix transformations (§4.9--4.10) MIDTERM #2
04.03–04.07 Eigenvalues and eigenvectors (§5.1)
04.10–04.14 Diagonalization and applications (§5.2–5.5)
04.17–04.21 Inner products (§6.1–6.2)
04.24–04.28 Least square (§6.4) MIDTERM #3
05.01–05.05 Numerical methods (§9.1, 9.4)
05.10 FINAL EXAM at 11:50 AM