Math 251: Matrix Algebra I - Fall 2007

Math 251: Matrix Algebra I - Fall 2007



Important Notes


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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!


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Midterm I

Here is the Midterm I and the Midterm I with solutions.

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.


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Midterm II

Here is the Midterm II and the Midterm II with solutions

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.


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Here is the final: Final, Final Solution.


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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:

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 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.


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.


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.


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Legal Issues


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

Academic Integrity

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.


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.  

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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.


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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!)


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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.


HW15 - Not due! Just work to prepare for final:

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, and I'll update it and let you know.


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