# Math 2331: Linear Algebra, Spring 2013

## Basic Info

Instructor: Dr. Mark Tomforde
Office: 601 PGH
Office Hours:

Monday, Noon--1:00PM
Wednesday, 2:30--3:45PM (right before class)
Lecture: MW 4:00--5:30PM in 103 SEC
ANNOUNCEMENTS: The Final Exam is Monday, May 6, 5PM--8PM
in our usual classroom.

## Exams and Homework

Homework:

Due Monday, April 29
Extra Problems to Help You Prepare for the Final Exam
(1) Extra Problems #1
(2) Extra Problems #2
(3) Extra Problems #3
(4) Extra Problems #4

Due Wednesday, April 17
Reading Assignment: Sec. 5.2, 5.3
Homework (Not To Be Handed In): Sec. 5.2 #1, 3, 5, 7, 9, 15, 19, 21; Sec. 5.3 #1, 3, 5, 7, 9, 11, 13, 15, 21, 23, 25, 27, 31, 32
Quiz #10 will be Wednesday, April 17. (Here are Solutions to Quiz 10.)

Due Wednesday, April 10
Reading Assignment: Sec. 4.7, 5.4, 5.1
Homework (Not To Be Handed In): Sec. 4.7 #1, 3, 5, 7, 9, 11, 13; Sec. 5.4 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23; Sec. 5.1 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32
Quiz #9 will be Wednesday, April 10. (Here are Solutions to Quiz 9.)

Due Wednesday, April 3
Reading Assignment: Sec. 4.4, 4.5, 4.6
Homework (Not To Be Handed In): Sec. 4.4 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 27, 29, 31; Sec. 4.5 #1, 3, 5, 7, 9, 11, 13, 19, 21, 23, 27; Sec. 4.6 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 27
Quiz #8 will be Wednesday, April 3. (Here are Solutions to Quiz 8.)

Due Wednesday, March 27
Reading Assignment: Sec. 4.1, 4.2, 4.3
Homework (Not To Be Handed In): Sec. 4.1 #1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25, 27, 29; Sec. 4.2 #1, 3, 5, 7, 11, 15, 17, 25, 27, 30, 31, 32, 33, 34; Sec. 4.3 #1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25, 29, 31, 33, 34, 35
Quiz #7 will be Wednesday, March 27. (Here are Solutions to Quiz 7.)

Due Wednesday, March 20
Reading Assignment: Sec. 3.1, 3.2
Homework (Not To Be Handed In): Sec. 3.1 #1, 3, 5, 7, 9, 13, 19, 21, 25, 27; Sec. 3.2 #1, 3, 5, 15, 17, 19, 21, 25, 27, 29, 31
Exam #2 will be Wednesday, March 20. (Exam #2 will cover all sections through Sec. 3.2.)

Due Wednesday, March 6
Reading Assignment: Sec. 2.8, 2.9
Homework (Not To Be Handed In): Sec. 2.8 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 31, 33; Sec. 2.9 #1, 3, 5, 9, 11, 13, 15, 17, 19, 21
Quiz #6 will be Wednesday, March 6. (Here are Solutions to Quiz 6.)

Due Wednesday, February 27
Reading Assignment: Sec. 2.4, 2.5
Homework (Not To Be Handed In): Sec. 2.4 #1, 3, 5, 7, 9, 11, 13, 21, 22, 25; Sec. 2.5 #1, 3, 5, 7, 11, 15
Quiz #5 will be Wednesday, February 27. (Here are Solutions to Quiz 5.)

Due Wednesday, February 20
Reading Assignment: Sec. 2.3, prepare for exam
Homework (Not To Be Handed In): Sec. 2.3 #1, 3, 5, 11, 13, 15, 17, 19, 21, 33
Exam #1 will be Wednesday, February 20.

Due Wednesday, February 13
Reading Assignment: Sec. 2.1, 2.2
Homework (Not To Be Handed In): Sec. 2.1 #1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23; Sec. 2.2 #1, 3, 5, 7, 9, 13, 17, 19, 21, 29, 31
Quiz #4 will be Wednesday, February 13. (Here are Solutions to Quiz 4.)

Due Wednesday, February 6
Reading Assignment: Sec. 1.9, 2.1
Homework (Not To Be Handed In): Sec. 1.8 #1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35; Sec. 1.9 #1, 3, 5, 7, 15, 17, 19, 21, 23, 35
Remember that, from this point on, in any True/False statements you should provide an explanation (or proof) when you claim the statement is true, and a counterexample when the statement is false.
Quiz #3 will be Wednesday, February 6. (Here are Solutions to Quiz 3.)

Due Wednesday, January 30
Reading Assignment: Sec. 1.7, 1.8
Homework (Not To Be Handed In): Sec. 1.5 #1, 3, 5, 9, 11, 13, 15, 23, 25, 27; Sec. 1.7 #1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 27, 31, 33, 35, 37, 39
Quiz #2 will be Wednesday, January 30. (Here are Solutions to Quiz 2.)

Due Wednesday, January 23
Reading Assignment: Sec. 1.4, 1.5
Homework (Not To Be Handed In): Sec. 1.4 #1, 3, 5, 7, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35
Quiz #1 will be Wednesday, January 23. (Here are Solutions to Quiz 1.)

Due Wednesday, January 16
Reading Assignment: Sec. 1.1, 1.2, 1.3
Homework (Not To Be Handed In): Do These Problems, also Sec. 1.1 #7, 9, 11, 13, 15, 19, 21, 23; Sec. 1.2 #7, 9, 11, 13, 15, 19, 21, 23, 25, 27, 29, 31; Sec. 1.3 #1, 5, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29
There will be no quiz this week.

First Day of Class
Here are copies of the items handed out on the first day of class:

Exam Dates:
Exam 1 -- Wednesday, February 20
Exam 2 -- Wednesday, March 20
Final Exam -- Monday, May 6, 5:00--8:00PM

## Miscellaneous Resources

• It will be important for you to read your textbook in this course. If you are unfamiliar with reading mathematics textbooks, here is a collection of Tips for Reading Your Mathematics Textbook that I have written.

• An online matrix calculator that you can use to check some of your matrix calculations.

• The history of mathematics is an important subject. It gives a context in which to view the results that one learns in math classes. Furthermore it shows that mathematics is, first and foremost, a human activity. In the historical development of Linear Algebra, we see that the concept of a vector dates back as early as the work of Bolzano in the beginning of the 19th century. Initially vectors were used in the study of geometry, giving a way to "coordinatize" space. Transformations on space often took the form of matrices, and this prompted the study of such matrix properties as determinants and canonical forms. Later, in the work of Poncelet and Chasles, a move was made to a coordinate-free, or synthetic, geometry. This was the beginning of the notion of an abstract vector space, in which one replaces concrete spaces by abstract spaces satisfying certain axioms, and in which matrices are replaced by linear operators on these spaces. Today the influence of Linear Algebra extends far beyond geometry, and the concept of an (abstract) vector space arises in a variety of contexts. Consequently, Linear Algebra has had applications to numerous areas of mathematics as well as many areas of physics.

Here you can find out more about:

• The Wikipedia entry on Linear Algebra.

• Some Linear Algebra Tools on the web.

• Also check out some unsolved problems in mathematics

and the various awards that are given to people working towards the solutions of these, and many other, problems in mathematics: