University of Connecticut College of Liberal Arts and Sciences
Department of Mathematics
Tom Roby's Math 2210Q Home Page (Spring 2014)
Applied Linear Algebra

Questions or Comments?

Class Information

COORDINATES: Classes meet Tuesdays and Thursdays 11:00-12:15 in MSB 215 The registrar calls this Section 003, #2644.

PREREQUISITES: MATH 1132, 1152, OR 2142.

TEXT: David C. Lay: Linear Algebra and Its Applications, 4th Ed., available in the bookstore. Let me know if you have any trouble getting it.

WEB RESOURCES: The homepage for this course is The author also has a useful site with review sheets and downloadable data here.

SOFTWARE: In most areas of mathematics it is frequently helpful to use computer software not only for computations, but also to explore examples, search for patterns, or test conjectures. For linear algebra there are several extensive and sophisticated commercial software packages, including MATLAB, Maple, and Mathematica. Matlab is particularly good at linear algebra for applications. All of these can be expensive, depending on your site license.

An excellent alternative to the above is the free open-source computer algebra system Sage. There are many commands for linear algebra, and a textbook (linked below) has been written that makes significant use of Sage examples. Sage also provides a full-fledged programming environment via the Python programming language, but you don't need to be a programmer to use it. I highly recommend trying it out online, and installing a copy on your computer.

GRADING: Your grade will be based on two midterm exams, a final exam, homework, and quizzes.

The breakdown of points is:

Midterms Final Quizzes Homework
20% each 30% 20% 10%

EXAMS: The exam dates are already scheduled, so please mark your calendars now (midterms in class on 27 February and 15 April at usual time; final [tentatively] on 6 May 2014, 10:30-12:30). All exams (like math itself at this level) are cumulative. No makeups will be given; instead if you have an approved reason for missing an exam, the final will count for the appropriately higher percentage.

QUIZZES: Quizzes will be given each Thursday (except midterm exam days), covering (a) sections from the previous week (at the level of HW exercises) and (b) the reading assigned for the current week (at the level of True/False exercises). Your lowest two quiz scores will be dropped.

HOMEWORK: Homework will be assigned most weeks, and is DUE at class the following TUESDAY. Since I may discuss the homework problems in class the day they are due, late assignments will be accepted only under the most extreme circumstances. Please let me know as soon as possible if you find yourself with a situation that might qualify. The lowest written homework score will be dropped in any event. I've color coded the schedule by week to help clarify what the HW is for a given week.

You may find some homework problems to be challenging, leading you to spend lots of time working on them and sometimes get frustrated. This is natural. I encourage you to work with other people in person or electronically. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. It also is a poor learning strategy.

ACADEMIC INTEGRITY: Please make sure you are familiar with and abide by The Student Code governing Academic Integrity in Undergraduate Education and Research. For quizzes and exams you may not discuss the material with anyone other than the instructor or offical proctor, and no calculators, phones, slide rules or other devices designed to aid communication or computation may be used unless otherwise specifically indicated on the exam.

CONTENT: Linear Algebra is a beautiful and important subject, rich in applications within mathematics and to many other disciplines. For many of you this is the first course to begin bridging the gap between concrete computations and abstract reasoning. Understanding the notions of vector spaces, linear (in)dependence, dimension, and linear transformations will help you make sense of matrix manipulations at a deeper level, clarifying the underlying structure.

ACCESSIBILITY & DISABILITY ISSUES: Please contact me and UConn's Center for Students with Disabilities as soon as possible if you have any accessibility issues, have a (documented) disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency.

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.

We will often spend classtime doing things in groups, presenting mathematics to one another, or having interactive discussions. There will not be time to "cover" all material in a lecture format so you will need to read and learn some topics on your own from the book (or otherwise).

SCHEDULE: I will update the following schedule over the course of the semester. Generally we will cover three sections per week, which means splitting a section between two lectures. Lecture notes are linked section by section: I recommend you review them before or after lecture, allowing you to spend lecture time focussing on the material rather than copying things down. If you have a religious observance that conflicts with your participation in the course, please meet with me within the first two weeks of the term to discuss any appropriate accommodations.

I've color coded the schedule by week to help clarify what the HW is for a given week.

Section Date Topics HW Problems
§1.1 1/21 T Intro to Linear Alg & Systems of Eqns. 1, 2, 3, 10, 12, 13, 15, 16, 21, 24, 25, 31, 32
§1.2 1/23 R Row Reduction & Echelon Forms 2, 10, 13, 14, 19, 21, 24, 29, 31
§1.3 1/23 R Vector Equations 3, 6, 7, 9, 12, 14, 15, 21, 22, 23, 25 due 1/30
§1.4 1/28 T Matrix Equations 1, 4, 7, 9, 11, 13, 17, 19, 22, 23, 25, 31
§1.5 1/30 R Solution Sets of Linear Systems 2, 6, 11, 15, 18, 19, 22, 23, 27, 30 HW 1.3 due
§1.7 2/4 T Linear Independence

1, 2, 5, 7, 9, 15, 16, 20, 21, 32, 35

§1.8 2/6 T Linear Transformations

2, 4, 8, 9, 13, 15, 17, 21, 26, 31

§1.9 2/6 R Matrix of Linear Transformation

1, 2, 5, 13, 15, 20, 23, 26, 32, 34

§2.1 2/11 T Matrix Operations and Inverses

2, 5, 7, 10, 15, 20, 22, 27, 28

§2.2 2/13 R Inverse of a Matrix

3, 6, 7, 9, 11, 13, 15, 23, 24, 29, 32, 37

§2.3 2/18 T Characterizations of Invertible Matrices

1, 3, 5, 8, 11, 13, 15, 17, 26, 28, 35, 40(challenge!)

§2.4 2/18 T Partitioned matrices

1, 4, 9, 10, 11, 13, 16, 19

Ch. 1 2/18 T Supplementary Exercises

6, 7, 10 ,18, 22, 23

§2.5 2/20 R Matrix Factorizations

2, 5, 7, 21, 23b, 24

§3.1 2/25 T Intro to Determinants

4, 8, 11, 13, 20, 21, 31, 32, 37, 39

§3.2 2/25 T Properties of Determinants

2, 3, 8, 10, 16, 17, 20, 26, 27, 32, 34, 40

§1.1–2.5 2/25 T Catchup & Review Day Do Practice Midterm by today!
§3.3 3/4 T Cramer's Rule & Volumes

4, 5, 6, 13, 16, 22, 23, 26, 29, 30; HW 2.5–3.2 due.

§4.1 3/4 T Vector Space & Subspaces

1, 3, 8, 12, 13, 15, 17, 22, 23, 31, 32

§4.2 3/6 R Null Spaces, Column Spaces & Lin. Transf.

3, 6, 11, 14, 17, 19, 21, 24, 25, 32, 33, 34, 36

§4.3 3/11 T Bases and Lin Ind. Sets

3, 4, 8, 10, 14, 15, 21, 23, 24, 29, 30, 31;

§4.4 3/13 R Coordinate Systems

2, 3, 5, 7, 10, 11, 13, 15, 17, 21, 23, 32 Midterm #1 rewrites due.

§4.5 3/25 T Dimension of a VS

1, 4, 8, 11, 14, 21, 23, 26, 28, 29

§4.6 3/25 T Rank

2, 5, 7, 10, 13, 19, 24, 27, 28;

§4.7 3/27 R Change of Basis

1, 3, 5, 7, 9, 11, 13, 15

§5.1 4/1 T Eigenvectors & Eigenvalues

2, 6, 7, 11, 13, 15, 19, 21, 23, 24, 25, 27, 31

§5.2 4/1 T Characteristic Equation

2, 5, 9, 12, 15, 19, 20, 21

§5.3 4/3 R Diagonalization

1, 4, 5, 9, 11, 15, 17, 21, 24, 26

§5.4 4/7 T Eigenvectors & Linear Transformations

1, 3, 6, 7, 10 ,15, 16, 23, 25

§6.1 4/7 T Inner Product & Orthogonality

3, 5, 10, 16, 18, 19, 23, 25, 27, 29

§1.1–5.2 4/10 R Catchup & Review Day Do Practice Midterm 2 by today
§6.2 4/17 R Orthogonal Sets

3, 6, 8, 9, 11, 14, 20, 21, 23, 26, 27, 28, 29 HW 5.4 and 6.1 due.

§6.3 4/22 T Orthogonal Projections

1, 6, 7, 9, 11, 13, 17, 21, 23, 24

§6.4 4/22 T Gram-Schmidt Process

1, 3, 7, 9, 11, 17, 19

§6.5 4/24 R Least-Squares Problems

3, 5, 7, 9, 11, 17, 19, 21

§7.1 4/24 R Diagonalization of Symmetric Matrices

1, 3, 5, 8, 10, 13, 17, 19, 25, 29

§7.2 4/29 T Quadratic Forms

1, 5, 8, 11, 13, 19, 21, 27

§7.3 4/29 T Constrained Optimization

1, 3, 5, 7, 11

§7.4 5/1 R Singular Value Decomposition

1, 3, 9, 11, 17

§1.1-7.4 5/1 R Catchup & Review Day
MONDAY 5 MAY 8:00PM–10:00PM FINAL REVIEW IN MSB 215 (Do Practice Final by today)

Web Resources

Anonymous Feedback

Use this form to send me anonymous feedback or to answer the question: How can I improve your learning in this class?  I will respond to any constructive suggestions or comments in the space below the form. 

Feedback & Responses

  1. [23 Jan] From today's notes, I'm having trouble understanding why columns 1,2, and 4 are the pivot columns.

    I tried to address this in class. The pivot columns are just the columns in which the pivots appear; perhaps the real question is identifying pivots?

  2. [26 Jan] Can you go over problem 12 from the 1.1 homework on Tuesday?

    I think we did this. You should always feel free to ask about HW problems at the start of class on Tuesday, and feel free to copy solutions I write into your HW. I probably won't post more questions like this, but will try to note them and go over them as requested.

  3. [29 Jan] I feel that, in the future, solutions to the practice quizzes should be posted. How do we know that we are prepared for the quiz if we can't check our answers?

    Thanks for asking. I posted (and emailed for safety) solutions to the practice quiz. There's only one, since I wanted everyone to have a sense of the format before the first one. The best way to prepare for the quiz is to spend more time with HW questions, particularly some of the true/false in each section. The text provides answers to most odd-numbered problems, so you can try some of those to check.

  4. [2 Feb] I do not understand almost any of the 1.5 homework. Is it still due on Tuesday even though we did not complete the section in class?

    Sorry you're having trouble with 1.5. We did finish the notes for that section on thursday, though. Please do the best you can on the HW and come to class tuesday with lots of questions! Perhaps this would be a good time to visit the Q Center?

  5. [2 Feb] Will solutions to quizzes be posted?

    Not usually, but we'll go over them in class after they are handed back. That allows me to address common issues and make connections that go beyond just the solutions. As always, if I don't address your specific concern, feel free to ask!

  6. [5 Feb] Practice quiz 2?

    Sorry, there was only a practice quiz #1, and that was over and above what I've done in previous semesters. There will also be practice midterms and finals. Best way to study for the quizzes is to go over homework problems (assigned and unassigned), particularly the True/False in each section.

  7. [8 Feb] Is there any way to get the solutions for the even numbered problems because it will be great to be able to check them without asking you to go over them in class which might waste class time if I ask to go over all the even numbered problems.

    Hmm. Some problems you can check yourself if they involve getting an answer you plug back in to check, but for others that won't work. It doesn't take long to go over just the answers without the solutions if there are some where you lack confidence in your answer. Buddying up with another student and comparing answers is also a good strategy. Unfortunately, in real life there is no solutions manual, so it's a good skill to learn to self-assess how likely you think it is you solved a problem correctly.

    Pedagogically I don't mind at all going over HW problems. It gives me a chance to address common confusions, and provides a forum for questions to come out. I don't think it's wasted time.

  8. [9 Feb] In class could we stress what terms mean more? I understand how to do things mathematically, but sometimes in the homework I don't quite know what they're asking because of the lingo.

    There's certainly a lot of terminology to wrap one's head around, especially in the beginning. I do try to give some of the intuition behind the various definitions as we discuss them. I'll look for opportunities to do more. Perhaps you could also make sure to ask about any specific HW lingo that you find confusing? Thanks!

  9. [10 Feb] Since you collect homework on Tuesdays, would it be possible to upload the answers to the problems (like the ones you were using to go over homework problems) or hand them out in class so we have something to study off of for the quiz on Thursday? It would also save class time if we could see the answers after handing in the homework with the steps to see our mistakes without having to use class time.

    Thanks for the suggestion. I now think a good solution to giving yourself something to study from is to just scan or snap a picture of your HW for reference before you hand it in. For various reasons, I think that handing out canned solutions raises more issues than it solves. Most even problems have an odd counterpart which you can try to solve and check against the answer. (See also my reply above to the feedback from 8 Feb.)

  10. [10 Feb] 30 problems for a homework seems a bit excessive, by the end it is feeling like busy work

    Sorry you feel that way. By all means feel free not to do problems which you're sure you know how to do, and could do on a quiz. I certainly would not want to waste anyone's time with exercises only for their fingers, not their brains. In my experience most students need to do a fair number of problems to master the various techniques. My basic assumption is that on average students spend about six hours per week doing HW and studying for a class that meets three "hours" per week. If you are finding you need significantly more than that, please see me, and I'll do my best to help!

  11. [10 Feb] Practice Midterm(s) + Final links do not work.

    Thanks for noticing! They become active as the practice tests become available. I just (on 11 Feb) posted the first practice midterm below, and the link in the schedule above should also work now.

  12. [15 Feb] Is the link for the take home quiz posted?

    Nope, it only went out by email. If you didn't get it, please email me directly! It means there's a glitch somewhere in the email system, which should get resolved asap.

  13. [18 Feb] Are the chapter 1 supplementary problems mandatory for the homework? Will we get penalized for not doing them?

    The main benefit to doing them, as with all HW, is that you'll improve your understanding of the material. This may translate later on to higher scores on quizzes or exams. Supplementary problems have the advantage of helping you integrate your knowledge from different sections. But as far as an explicit penalty goes, it would be at most 1–2 points out of five on that week's HW, which is negligble in the scheme of things.

  14. [5 Mar] What was the mean score on the test?

    Mean and median were both mid-sixties. I'll bring the exact values to class tomorrow. With the rewrites, if you all take them seriously, I expect it to be much higher, probably in the 80s.

  15. [10 Mar] We did not take any notes on 3.3. I took some myself from the book but I don't feel there are a sufficient amount of examples to do the homework. I am fairly confused on almost every problem.

    I hope this means that you generally like the notes provided for most sections as an outline of lecture! Still, it's good to learn how to seek other resources when the ones you used so far are insufficient. These include:

    • Googling the topic and seeing what you find in the way of wikipedia entries, notes made by others, or videos that show things step by step;
    • Discussing things with a classmate or student who may already have had the course;
    • seeking help at the Q Center;
    • emailing the instructor specific questions;
    • asking on Facebook or other social media;
    • asking in class during the time dedicated to this;
    Of course, I can try to eventually create notes for this section or try some other way to make this material more accessible—that's easier for me if I understand what students are confused about. But the broader point of becoming more independent in your learning is a life skill that will serve you well at UConn and beyond.

  16. [15 Mar] Did enough people hand in Quiz 5 for everyone to get full credit for it?


  17. [21 Mar] Very useful.


  18. [23 Mar] Do we have homework due this Tuesday?

    Yes, for §4.3-4 as indicated on the syllabus.

  19. [15 Apr] Which homework is due Thursday?

    All the homework from last week, which would ordinarily have been due on Tuesday, specifically §5.4 and 6.1.

  20. [16 Apr] I love the simple layout of the notes with minimal words. They don't give too much which is overwhelming or too little that I can't make the connections from step to step. Keep it simple.

    Thanks! The Goldilocks Principle in action.

  21. [17 Apr] Would we have a quiz the Thursday after the midterm?

    No. The midterm is enough testing for one week.

  22. [Date] This is a test.

    This is only a test.


[16 Feb] I sent an email on 13 Feb to the entire class with (a) the take-home quiz #3 and (b) a link to a video lecture for §2.2. Please email me if you didn't get it! Notice also that the first practice midterm is now posted.

[23 Feb] Practice Midterm 1 Solutions are now posted. Homework for sections 3.1 and 3.2 postponed until the Tuesday after the exam. We'll go over those sections (which are computational and straightforward) briefly this Tuesday, 2/25 before starting the review (revised schedule above).

[5 Mar] Rewrites for Midterm #1 are due Thursday 13 March in class. Please follow the guidelines in the handout below. This is a great opportunity to learn the material you missed and improve your grade.


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