Math 251: Matrix Algebra I - Fall 2007

GO TO:

## Important Notes

• (12/03 - 6:35pm) I have just finished writing the final exam. Here is some info about it:

• It is on Wednesday (12/12), from 12:30pm to 2:30pm in our regular classroom.
• It covers everything, more precisely, sections 1.1-7, 2.1-3, 3.1-3, 4.1-3, 5.1-6, 6.1-2, 6.3 except Gram-Schmidt and QR-decomposition, 6.5, 7.1-3.
• The exam has 6 questions. Three single part, worth 10 points each, and three with four parts, worth 22, 24, and 24 points. Most of them deal with concepts from Chapters 5, 6, and 7, but you will also need the tools from the previous chapters to work them out.
• I think that you could do this exam comfortably in one hour and a half, so I assume that you don't have to hurry to much. (You will have the two full hours to work on it.) But, as with the other exams, you have to know the theorems that make things simpler, or you might waste too much time. (Keep in mind that sometimes is hard for me to estimate how much time you will need, but I do believe you will have plenty of time.)
• Also, this exam will more computational than the previous. So I believe it will not be too hard.
• I will have office hours on Tuesday (12/11) at 11am (in my office, Ayres 212D). If you need to see me but cannot come at that time, please write me an e-mail to make an appointment.
• NO CALCULATORS WILL BE ALLOWED!
• To study, I recommend:
• Quickly review your notes and read the book. The most important parts is to review the definitions, Theorems, and techniques (e.g., how to show something is linearly dependent/independent, a basis, spans, etc.). If necessary, write those in a different sheet of paper so that you don't have to browse your book every time you need to refresh your memory.
• Look at all examples and solved problems. As I've mentioned in class a few times, I posted more detailed solutions for our last HW sets. Make sure to look at them carefully!
• Review your old HWs and midterms. Redo all problems that you've missed. (You should always learn from your mistakes!) Always look for exactly what went wrong so that you do not repeat the same mistake!
• Look in solutions of solved problems for ideas that can make a calculations shorter or simpler. Even if you can compute it right, there might be a faster way.
• Do as many problems as possible from the book.
• When you first start studying, you can look at the book or notes, but by the end, you should be able to do problems without looking.
• Try to choose six to eight problems from different sections to work on as if you were in the exam: no notes, allow only 2 hours, etc. This might give you an idea if you are prepared.
• (08/20 - 12:00pm) Please, check this section often. I will put announcements and important info here.

• (08/20 - 12:00pm) Please, hit the ``Refresh'' or ``Reload'' button on your web browser every time you visit this page, so that you can see the most recent updates.

Back to the TOP.

### Instructor Contact and General Information

Instructor: Luís Finotti

Office: Ayres Hall 212-D

Phone: 974-1321 (please do not ask me to call back -- leave your e-mail)

Office Hours: MWF 11:15am-12:15pm or by appointment (subject to change!!)

Textbook: H. Anton, ``Elementary Linear Algebra'', 9th Edition. Wiley, 2004. (The ``Applications Version'' of this book is also OK, but more expensive and unnecessary.)

Prerequisite: Math 142 or Math 148.

Class: MWF 12:20-1:10 at Ayres Hall 318. (Section 2.)

Exams: Midterms: 09/28 (Fri) and 11/05 (Mon), in regular classroom and time; Final: 12/12 (Wed) from 12:30pm to 2:30pm, also in our regular classroom.

Grade: 20% for HW + 20% for each Midterm + 40% for the Final. Note the weight of the HWs!

Back to the TOP.

### Exams:

#### Midterm I

The exams were graded and will be returned in class on Monday (10/01). (You can check your grades in Blackboard.) If you are not in class that day, you have to come by my office to pick up yours. (I will not take them to class anymore.) The average was 61, the median was 64 and the highest grade was 94. So, the results were quite bad, considering that the exam was easy. (Just check the solutions (when posted).)

Note that the last day to drop the course with a W is tomorrow (10/02)!! I am not suggesting that anyone should drop (we still have plenty of points), but you should consider that it's likely that the course will only get more difficult.

Here is how I would curve these grades and the number of people with each grade:

 Grade Range # of people A 90-100 1 B+ 83-89 3 B 77-82 3 C+ 70-76 4 C 60-69 10 D 50-59 3 F < 50 7

Note: This curve is just to give you an idea of how I curve. In the end I will not even look at this curve, I will just curve all the final averages.

Back to the TOP.

#### Midterm II

The exams were graded and will be returned in class on Wednesday (11/07). (You can check your grades in Blackboard.) If you are not in class that day, you have to come by my office to pick up yours. (I will not take them to class anymore.) The average was 54, which is way too low, and the highest grade was 81, and I expected better of some of you.

Here is how I would curve these grades and the number of people with each grade:

 Grade Range # of people A 79-100 2 B+ 75-78 2 B 65-74 3 C+ 55-64 6 C 50-54 7 D 45-49 0 F < 45 5

Note: This curve is just to give you an idea of how I curve. In the end I will not even look at this curve, I will just curve all the final averages.

Back to the TOP.

#### Final

Here is the final: Final, Final Solution.

Back to the TOP.

### Course Information:

This is a first course on Linear Algebra. We will study matrix algebra, system of linear equations, vector spaces, linear transformations, and eigenvalues/eigenvectors.

The first two of these topics are of computational nature, while the latter topics will be more theoretical, and hence usually considered harder by the students. Therefore, the initial plan is to go rather fast through the computational material, so that we can go over the most challenging topics on a better pace.

#### Course Structure

We will likely cover the following:

• Chapter 1: sections 1-7.
• Chapter 2: sections 1-4.
• Chapter 3: sections 1-3.
• Chapter 4: sections 1-3.
• Chapter 5: sections 1-4.
• Chapter 6: sections 1-3 (no Gram-Schmidt or QR-decomposition), 5.
• Chapter 7: sections 1-3.

The first three chapters will be covered in a faster pace. Chapter 4 might also be covered superficially and briefly. The last three chapters should be the more challenging ones, I hope to have enough time to cover them in a slower pace.

Also, note that this outline is subject to change slightly without prior notice.

#### Homeworks

Homeworks will be assigned after every class and will be posted at the section Homework of this page. No paper copy of the HW assignments will be distributed in class. It is your responsibility to check this page often!. Besides HW assignments, other important information will be posted here. (Check the section Important Notes often!)

The HWs will be collected on Mondays (except on Labor's Day week, when it will be due on Wednesday). Each HW will have problems from the previous week (Monday, Wednesday and Friday lectures). The problems to be turned in, as well as due dates, will be clearly posted here. Note that not all of the problems turned in will be graded, but you won't know which until you get them back.

No late HWs will be accepted, except in extraordinary circumstances which are properly documented.

It is your responsibility to keep all your graded HWs and Midterms! It is very important to have them in case there is any problem with your grade.

I will do my best to post solutions. If I do, they will be posted in this page.

If I find a student copying solutions from the Solutions Manual of the book, he/she will get a zero in the assignment, and I will report him to the Office of Student Judicial Affairs. Obviously, the same goes for any other kind of cheating. (See the section Legal Issues below.)

In my opinion, doing the HW is one of the most important parts of the learning process, so the weight for them is equal to the weight of a single midterm, and I will assume that you will work very hard on them.

Also, you should try to come to my office hours if you are having difficulties with the course. I will do my best to help you. Please try to come during my scheduled office hours, but feel free to make an appointment if that would be impossible.

#### E-Mails

You will have to check your e-mail at least once a week, preferably daily. I will use your e-mail (given to me by the registrar's office) to make announcements. If that is not your preferred address, write me an e-mail letting me know ASAP. I will assume that any message that I sent via e-mail will be read in a week or less, and it will be considered an official communication.

#### Feedback

I have an On-line Feedback Form where you can anonymously send me your comments and suggestions. I will consider your comments and try to do whatever I can to resolve possible problems before it is too late. So, please, feel free to use it whenever you have any constructive comment or suggestion. (In fact, I would greatly appreciate it.) If you don't want you comments to be anonymous, just send me an e-mail or come by my office and we can discuss the problem.

Back to the TOP.

### Legal Issues

#### Conduct

All students should be familiar and maintain their Academic Integrity: from
Hilltopics 2007/2008, pgs.39-40:

The responsibility for learning is an individual matter. Study, preparation and presentation should involve at all times the student's own work, unless it has been clearly specified that work is to be a team effort. Academic honesty requires that all work presented be the student's own work, not only on tests, but in themes, papers, homework, and class presentation. There is a clear distinction between learning new ideas and presenting them as facts or as answers, and presenting them as one's own ideas. It is part of the learning process to incorporate the thoughts or ideas of others into one's own mind and presentations with the purpose of learning and enlarging on personal boundaries of knowledge.

All students should follow the Honor Statement: from Hilltopics 2007/2008, pg. 11:

Honor Statement

``An essential feature of The University of Tennessee is a commitment to maintaining an atmosphere of intellectual integrity and academic honesty. As a student of the University, I pledge that I will neither knowingly give nor receive any inappropriate assistance in academic work, thus affirming my own personal commitment to honor and integrity.''

You should also be familiar with the Classroom Behavior Expectations.

#### Disabilities

Students with disabilities that need special accommodations should contact the Office of Disability Services and bring me the appropriate letter/forms.

#### Sexual Harassment and Discrimination

For Sexual Harassment and Discrimination information, please visit the Office of Equity and Diversity.

Back to the TOP.

### Important dates:

Wednesday, August 22 - Classes begin.

Friday, August 31 - Last day to add, change grade options, or drop a full semester course without a "W".

Monday, September 03 - Labor Day Holiday. (No class.)

Friday, September 28 - Midterm I.

Tuesday, October 02 - Last day to drop a full term course with a "W".

Thursday-Friday, October 11-12 - Fall Break. (No class.)

Monday, November 05 - Midterm II.

Tuesday, November 13 - Last day to drop with a WP/WF.

Thursday-Friday, November 22-23 - Thanksgiving. (No class.)

Tuesday, December 04 - Last Class Day.

Wednesday, December 12 - Final.

More dates.

Back to the TOP.

Back to the TOP.

Back to the TOP.

### Solutions to Selected HW Problems

Please read: I will try to post here a few solutions. The new solutions will be added to this same file. They might come with no explanation, just the ``answer''. If yours do not match mine, you can try to figure out again. (Also, read the disclaimer below!) You can come to office hours if you want explanations for the answers. Be careful that just because our ``answers'' were the same, it doesn't mean that you solved the problem correctly (it might have been a ``fortunate'' coincidence), and in the exams what matters is the solution itself. I will do my best to post somewhat detailed solutions to the harder problems, though.

Disclaimer: I will have to put these solutions together rather quickly, so they are subject to typos and conceptual mistakes. (I expect you to be a lot more careful when doing your HW than I when preparing these.) You can contact me if you think that there is something wrong and I will fix the file if you are correct.

Solutions to Selected HW Problems (Click on ``Refresh'' or ``Reload'' if you don't see the changes!)

CHANGE LOG:

• (11/29 - 2:35pm) Posted solutions for HW15.
• (11/28 - 7:35pm) Posted solutions for HW14.
• (11/20 - 12:45pm) Posted solutions for HW13.
• (11/13 - 5:00pm) Posted solutions for HW12.
• (11/01 - 6:30pm) Posted solutions for HW11.
• (10/29 - 10:20pm) Posted solutions for HW10.
• (10/24 - 6:35pm) Posted solutions for HW9.
• (10/18 - 5:00pm) Posted solutions for HW8.
• (10/16 - 2:50pm) Posted solutions for HW7.
• (10/02 - 11:50am) Posted solutions for HW6.
• (09/26 - 7:30pm) Posted solutions for HW5.
• (09/19 - 6:30pm) Posted solutions for HW4.
• (09/14 - 2:30pm) Posted solutions for HW3.
• (09/09 - 11:50pm) Posted solutions for HW2.
• (09/01 - 10:20pm) Fixed typo on 1.2.21.
• (08/29 - 11:50am) Posted solutions for HW1.

Back to the TOP.

### Homework

HW1 - Due on Monday 08/27:

Section 1.1: 1, 2, 3(a), (b), 4(a), (c), 5(a), (c), 6, 11, 12, 13.

Section 1.2: 1, 3, 5(a), (c), 6(b), (d), 7(b), 8(b), 10(b), 12, 14(a), (b), 17, 21 (typo: it should read "12 solutions", not 18), 22.

HW2 - Due on Wednesday 09/05:

Section 1.3: 1, 2, 3(g), (j), (k), 5(a), (b), (d), (h), (j), 7(a), (d), (e), 8, 12(b), 13(a), 14(a), 18(a), 21.

Section 1.4: 1(b), (d), 3(d), 4(b), 5(b), 6(a), 7(c), (d), 9(b), 13, 14, 17, 20(b), 21, 29.

HW3 - Due on Monday 09/10:

Section 1.5: 1, 3, 5, 7(a), (d), 9, 14, 15.

Section 1.6: 2, 7, 11 (you can use any method here), 15, (16 and 17 were postponed!!) 23.

HW4 - Due on Monday 09/17:

Section 1.6: 16, 17.

Section 1.7: 1, 2, 4, 5, 11, 12, 13 (only matrix A), 15, 18.

Section 2.1: 3(a), (d), 4, 7, 12, 13, 17.

Section 2.2: 1(b), 2, 3, 4, 6, 9, 12, 14(a).

HW5 - Due on Monday 09/24:

Section 2.3: 2, 4, 5, 6, 7, 12, 14(a), (b), 15(a), (b) (this means use only (a) and (b) from 14 in 15), 16.

Section 3.1: 6, 7, 8, 9, 10, 11.

Section 3.2: 1(a), (e), 2(a), (c), 3, 4, 7.

Section 3.3: 1(a), (d), 2(a), (d), 3, 4(a), (c), 5(a), (c), 9, 12, 16.

HW6 - Due on Monday 10/01:

Section 4.1: 3, 7, 9(d), 11(c), 14(d), (e), 16, 18(b), 20.

HW7 - Due on Monday 10/08:

Section 4.2: 1, 3, 5, 7, 9, 12 16, 20.

Section 4.3: 1, 2(b), (c), 4, 5(b), 6(b), 7, 8, 11, 13, 15.

HW8 - Due on Monday 10/15:

Section 4.3: 19(a), (c), 22.

Section 5.1: 1, 5, 6, 7, 9, 11, 12, 15, 18.

HW9 - Due on Monday 10/22:

Section 5.2: 1, 2(b), (c), 3(c), (d), 4(a), (b), (c), 5(b), (c), 7, 8(a), 10(c), (d), 11(a), (b), 13.

Section 5.3: 1, 3(a), (c), 5, 6(a), (b), 8, 9, 11, 13, 15.

HW10 - Due on Monday 10/29:

Section 5.4: 1, 3(a), (c), 4(a), (c), 7(b), (c), 8(c), 9(b), 10(b), 14, 16, 18(b), (c), 19, 23.

HW11 - Not to be turned in! (Just work on it to prepare for the exam!):

Section 5.5: 2(c), (d), 3(b), (c), 5(b), 6(c), 7, 8(c), 9(c), 11(b), (c), 12(c), 13.

HW12 - Due on Monday 11/12:

Section 5.6: 2(b), (c), 3(b), (c), 4, 5, 7, 8, 9, 12, 13.

HW13 - Due on Monday 11/19:

Section 6.1: 3(a), 4(a), 6, 8(b), 9(a), (d), 10(c), 11, 13(a), 14, 16(c), (f).

Section 6.2: Read: Theorem 6.2.6 and Example 6 from the book. Problems: 2, 4, 6(a), 8(a), 11, 15, 18(b), (c), 21.

HW14 - Due on Monday 11/26:

Section 6.3: 3, 4, 6, 8, 9, 11, 13, 14.

Section 6.5: 2, 4, 5, 6, 9, 11.

Section 7.1: 4(a), (c), (f), 6(a), (c), (f), 7, 9, 10, 11, 20.

Section 7.2: 1, 2, 6, 7, 9, 13, 16, 17, 19.

Section 7.3: 1(b), (c), (e), 3, 5, 7, 9.

And that's all!!

PLEASE, HIT ``REFRESH'' (OR ``RELOAD'') IN YOUR BROWSER WHEN VISITING THIS PAGE!!!!!!! I usually get messages asking for the update in the HW when it has already been updated. Since I change this page often, some times the browser don't see the changes. But, if you hit refresh and there is still problems missing, feel free to write me.

If it is already Friday afternoon and there still is a ``More to come'' after the HW assignment due on the coming Monday, write me an e-mail at lfinotti@utk.edu, and I'll update it and let you know.

Back to the TOP.