# Linear Algebra, Fall 2015

Course: MATH 2270, Section 002
Time/Place: M,W,F 12:55 - 1:45 PM in ST 208; T 12:55-1:45 PM in LCB 225
Instructor: Thomas Goller
Course book: "Linear Algebra and its Applications(Fifth Edition)"; by Lay, Lay, and McDonald; ISBN: 978-0321982384.
Problem Sessions: M 4:45-6:15 PM in JWB 333; H 12:55-1:45 PM in LCB 225
Office Hours: By appointment, in JWB 307.

Timeline
Solutions to odd exercises from 1.1-1.7 of the 4th edition
1.1-1.7 of the 4th edition
Syllabus

# Announcements

Thank you for putting up with me for a full semester. I hope you will find linear algebra to be useful in the future. And remember to staunchly oppose logging in the old-growth forests of the Pacific Northwest so that the spotted owls can survive!

I will have office hours from 11 AM to 3 PM on Monday, December 21, if you want to look over your final exam or talk about your grade. If you can't make that time you can also email me to make an appointment. If you ever have questions about which math classes to take and from whom you should take those courses, or if you just want to chat, you are welcome in my office.

Final letter grades are posted on CIS!

Here is the final table of total scores. In particular, you will find your final exam score listed in the table. The total percentage takes into account all scores from quizzes, tests, and the final exam. If you want to check that I have computed your total percentage correctly, add up all points from the five exams, your seven highest quiz scores, a bonus point if you got one, and your final exam score weighted by a factor of 2, and then divide by 500. Let me know if you have any questions.

Here are solutions to last year's final exam.

Here is last year's final exam, which should give you a good idea of the format and content of this year's final exam. Be aware that the notation and the topics covered this year and last year are similar but not identical.

To help you study for the final exam, here is a study guide for the Final Exam and a compilation of all test questions this year.

Here is a table of approximate grades after Test #5. Look up your line in the table using your test scores. The highest total percentage possible so far is 60. Explanation: 250 points from five tests; 50 points from nine quizzes because the lowest two are dropped; 500 points possible by the end of the year; for a current maximum percentage of (250+50)/500=.60. The total percentages listed in the table take into account all five tests, all nine quizzes (with the lowest two dropped), and bonus points, even though only the test scores are shown. Feel free to ask me if you have any questions!

I will soon post a table of approximate current grades as well as a study guide for the final exam.

There will be three review sessions for the final exam: Monday, December 14, 1-3 PM in LCB 222; Tuesday, December 15, 1-3 PM in LCB 222; Thursday, December 17, 3:30-5:30 PM in LCB 222. If you can't make the review sessions, I encourage you to email me to set up an appointment. By going over your past tests, I can give you tips for how to improve on the final exam.

Investigate these solutions to Test #5 and ask me if you have any questions about the solutions or about how I graded your test. I will be happy to talk about test questions during this week's Thursday problem session.

Reading assignments for Monday's lecture: Brady Mathews' project on image compression using the SVD (try to make sense of the figures!) and Sections 1 and 3 of "The Extraordinary SVD", by Carla Martin and Mason Porter.

The hour is late; solutions to Quiz #9 await.

As you begin studying for Test #5, carefully peruse this study guide for Test #5. Ask me if you have questions!

Quiz #9 (the last quiz!) will be on Tuesday, December 1 in LCB 225 and will cover Sections 6.4, 6.5, and 6.6.

Recommended problems for Test #5, from the 5th edition, are Section 7.1: 13, 17, 19; Section 7.4: 5, 7, 9, 11, 13.

I'm happy to share these solutions to Quiz #8.

Quiz #8 will be on Tuesday, November 24 in LCB 225 and will cover Sections 6.1, 6.2, and 6.3. Know how to compute orthogonal projections!

Recommended problems for Quiz #9, from the 5th edition, are Section 6.4: 1, 3, 5, 7, 9; Section 6.5: 1, 3; Section 6.6: 1, 2, 3, 4. Happy four-day break!

Please peruse these solutions to Test #4 and ask me if you have any questions about the solutions or about how I graded your test! The material on Tests #3 and #4 will be critical for the final exam! I will be happy to talk about test questions during this week's Thursday problem session.

Test #4 will be on Tuesday, November 17 in LCB 225. Please see the study guide for details. Bring your questions to Monday's review session!

Recommended problems for Quiz #8, from the 5th edition, are Section 6.1: 1, 3, 5, 7, 9, 13, 17; Section 6.2: 1, 7, 9, 11, 15, 17, 19; Section 6.3: 1, 3, 7, 11, 13, 15, 17.

The Monday review session will be held at the usual time and place. I do not have jury duty on Monday.

Here are solutions to Quiz #7.

Please read through this study guide for Test #4. Come to the review session on Thursday this week because I may not be able to hold a review session on Monday!

Quiz #7 will be on Tuesday, November 10 in LCB 225 and will cover Sections 5.1, 5.2, and 5.3. Be ready to compute eigenvalues and eigenvectors!

Friday's lecture will be about Google's famous "Page Rank" algorithm, which heavily uses linear algebra! In preparation, please try to read the article "The \$25,000,000,000 Eigenvector: The Linear Algebra Behind Google", which you can find online (by using Google search!).

Recommended problems for Test #4, from the 5th edition, are Section 5.4: 5, 9, 11, 13, 15, 17; Section 5.6: 1, 3, 5, 7, 9, 11, 13, 17a-b. Feel free to use Wolfram Alpha or other software to compute eigenvalues and eigenvectors for the exercises in Section 5.6.

Read these solutions to Quiz #6!

Quiz #6 will be on Tuesday, November 3 in LCB 225 and will cover Sections 4.7 and 4.9.

Recommended problems for Quiz #7, from the 5th edition, are Section 5.1: 3, 4, 5, 9, 11, 13, 25, 29, 31, 32; Section 5.2: 1, 3, 9, 11, 15, 18; Section 5.3: 1, 5, 7, 9, 11, 13, 15, 23, 31, 32. Most of the problems are straightforward: just follow the algorithm to compute eigenvalues and eigenvectors. Practice is essential to be sure that you can do this quickly!

Here is a table of approximate grades after Test #3. Look up your line in the table using your three test scores. The highest total percentage possible so far is 34.4. Explanation: 150 points from three tests; 22 points from three quizzes because the lowest two of the five are dropped; 500 points possible by the end of the year; for a current maximum percentage of (150+22)/500=.344. The total percentages listed in the table take into account all three tests, all five quizzes, and bonus points, even though only the test scores are shown. Feel free to ask me if you have any questions!

Carefully study these solutions to Test #3 and ask me if you have any questions about the solutions or about how I graded your test! The material on Test #3 will be critical for the final exam, so try to understand everything on the test. I will be happy to talk about test questions during this week's Thursday problem session.

Recommended problems for Quiz #6, from the 5th edition, are Section 4.7: 1, 5, 7, 9, 13, 14; Section 4.9: 1, 2, 3, 4, 11, 12, 13, 14. This is a short assignment, but Section 4.7 is confusing, so make an extra effort to understand it! Review the worksheet too.

Test #3 will be on Tuesday, October 27. Please see the study guide below for details!

Here is a detailed study guide for Test #3. Study hard and don't get intimidated!

Recommended worksheet on coordinates and linear transformations for Test #3.

Make sure you understand these solutions to Quiz #5! These concepts will be important for Test #3.

Quiz #5 will be on Tuesday, October 20 in LCB 225 and will cover Sections 4.1, 4.2, and 4.3.

Recommended problems for Test #3, from the 5th edition, are Section 4.4: 1, 3, 5, 7, 9, 11, 13, 21, 27, 31, 32; Section 4.5: 1, 9, 11, 13, 21, 23; Section 4.6: 1, 3, 5, 9, 13, 15, 25, 27.

Your search for solutions to Quiz #4 has come to an end.

Recommended problems for Quiz #5, from the 5th edition, are Section 4.1: 1, 2, 3, 5, 7, 9, 11, 13, 15, 21; Section 4.2: 5, 15, 31, 32; Section 4.3: 1, 3, 5, 7, 9, 11, 12, 19, 26, 33, 34. Quiz #5 will be on the first Tuesday after Fall Break.

Look over these solutions to Test #2 carefully and ask me if you have any questions about the solutions or about how I graded your test! I will be happy to talk about test questions in this week's Thursday problem session.

Recommended problems for Quiz #4, from the 5th edition, are Section 3.1: 1, 3, 9, 11, 37; Section 3.2: 1, 3, 5, 7, 15, 21, 25, 31, 39; Section 3.3: 19, 23, 25, 27, 29, 31, 32.

Test #2 will be on Tuesday, September 29. Please see the study guide below for details!

Here is a study guide for Test #2. I don't promise that it is comprehensive. (No changes were made to the study guide since it was first posted.)

The problem session on Thursday, September 4, has been cancelled. Sorry!

The timeline has been updated. We will cover Sections 2.1, 2.2, and 2.3 this week. After some thought, I've decided to skip Sections 2.4 and 2.7 entirely, since they don't seem to fit in the development of the material very well. This will give us more time for Section 2.3, which (like the equivalences I wrote on the board last Friday) draws connections between all the major concepts we've discussed so far in the course.

Quiz #3 will be on Tuesday, September 22 in LCB 225 and will cover Sections 1.9 and 2.1.

Recommended problems for Test #2, from the 5th edition, are Section 2.2: 1, 5, 13, 15, 29, 31, 37; Section 2.3: 13, 15, 17, 19, 27, 33. Also (and most importantly!), check all parts (a through l) of the "Invertible Matrix Theorem" for the matrices in Section 2.3 Exercises 1, 2, 3, and 4 (we will do an example of this in Friday's lecture).

Please read this response to some common concerns that you shared after Quiz #2.

Here are solutions to Quiz #2.

Quiz #2 will be on Tuesday, September 15 in LCB 225. The quiz will cover Sections 1.7 and 1.8. Work on the recommended problems from those sections!

Recommended problems for Quiz #3, from the 5th edition, are Section 1.9: 1, 3, 5, 11, 13, 17, 19, 25, 27, 29, 30, 35; Section 2.1: 1, 3, 5, 9, 15, 21, 23, 25 and Practice Problem 1.

The timeline has been updated. We will cover Section 2.2 next week, along with Sections 2.3, 2.4, and 2.7 (Sections 2.3 and 2.4 will be extremely brief.)

Recommended problems for Quiz #2, from the 5th edition of the textbook (that's right, we are no longer using the 4th edition!), are Section 1.7: 1, 7, 9, 15, 19, 23, 27, 29, 31, 33, 35, 37, 40; Section 1.8: 1, 5, 13, 14, 15, 16, 17, 18, 19, 21, 25, 31, 33. The list of problems looks endless, but many of them are quite short!

I strongly encourage you to come to Thursday's problem session if you are confused by many of the test questions. I will go over any test problems people want to see. If you are not happy with your score, come talk to me and I can look over your test and give you suggestions for how you can better prepare for the next test. The sooner you come see me the better!

Please study these solutions to Test #1 and ask me if you have any questions!

There will be a problem session on Monday from 4:45-6:15 PM in JWB 333 (usual time and place). Enter JWB through the east door after going up the stairs from the President's Circle sidewalk. I will prop open the door if it is locked.

Test #1 will be on Tuesday, September 8 and will fill all 50 minutes of class. It will cover everything we have done (Sections 1.1 to 1.5). Study the recommended homework problems and Quiz #1 and pay particular attention to the concepts I've emphasized in lecture. The format will be similar to the format of my tests last year, which you can find under the "Fall 2014, Math 2270" link on my homepage (I don't recommend studying these tests carefully because we used a different book last year and some of the material is different). There will be some problems with multiple parts; if you get stuck on an early part of a problem and can't continue without an answer, feel free to make up a reasonable answer (clearly labeling your answer as made up) so that you can do the later parts of the problem. While preparing for the quiz, please do extra problems to practice the techniques and concepts you find the most difficult, and come to the problem session if you have questions!

Here are solutions to Quiz #1.

Quiz #1 will be on Tuesday, September 1 in our usual Tuesday room (LCB 225). We'll start the quiz at the beginning of class so please come on time!

Recommended problems for Test #1, from the 4th edition of the textbook, are Section 1.4: 1, 5, 9, 13, 15, 21, 29, 30, 32; Section 1.5: 1, 5, 7, 11, 13, 15, 17, 19, 33, 35.

Recommended problems for Quiz #1, from the 4th edition of the textbook, are Section 1.1: 1, 7, 11, 13, 19; Section 1.2: 1, 3, 7, 11, 21, 23, 25, 28, 30, 31; Section 1.3: 5, 7, 11, 17, 19, 22, 32. If you still aren't comfortable with the row reduction algorithm, then please do more exercises in the book to practice! Row reduction will be important all semester long.

We will be using the 4th edition of the textbook for the first two weeks of the course. I expect you to have the 5th edition by the start of the third week. Please let me know if this is a problem!

Welcome!