xxx
Washington University in St. Louis

Math 309, Matrix Algebra
Section 1, Fall 2007
 
Note: Sections 1 and 2 of Math 309 use the same textbook and will cover nearly the same "core topics" that make up most of the course.  The sections may vary a bit in emphasis and on a few optional topics.  This syllabus applies only to Section 1 .

Instructor:  Professor Ron Freiwald 
Office: Cupples I, Room 203A, 935-6737
Office Hours:  (Beginning week of 9/3)    M 2:30-3:30, W 1:30-2:30, F 12:30-1:30 and by appointment

Class Time:        M-W-F 10-11 a.m..
Location:           Cupples I, Room 113

Textbook & Related Resources

Linear Algebra and Its Applications, by David Lay
This text is very well written and is a must-read as the course moves along. 

A copy of the Study Guide is bundled with your textbook at the Campus Bookstore. The Study Guide is a very valuable resource.  I recommend that you consistently use it as you work your way through the course.  In particular, read carefully the note on How to Study Linear Algebra at the beginning of the Study Guide.  If you are purchasing your books through a different source, the Study Guide, though very useful, is optional.

There is some good supplementary material at the Companion Web Site for the course (http://www.laylinalgebra.com/).  In particular, there's a large collection review sheets and practice exams from the author.  (The practice exams may or may not be what our exams look like, but they certainly provide a good self-test on some of the material.)

You can also look at whatever material is available at MyMathLab: registration material is included with the textbook.
                                                                  Course Bulletin Board

Final Exam Solutions

Spreadsheet containing total score for homework, quizzes, exams, and course total score.
 

Old handouts related to diagonalization:
Introduction to Diagonalization
Linearly Independent Sets of Eigenvectors
Some Equivalents of Diagonalizability
Relation of Eigenspace Dimension and Multiplicity of Eigenvalues
Relation of Diagonalizability to Characteristic Polynomial and Eigenvalues
Error in Theorem in Text on Diagonalizability and a Correction
Real 2x2 Matrices with Complex Eigenvalues.

Orthogonally Diagonal Matrices and the Spectral Theorem



Homework

Each  week (beginning in week 2) I will post here a list of assigned homework to be handed in.  These assignments will normally be due in class on Fridays.  Late homeworks usually will not be accepted unless there is a special legitimate reason such as illness.   When the problem list is first posted here it may not be complete.  However, the list of problems due the following Friday will always be complete by noon on the preceding Tuesday.  Be sure to check after Tuesday that you have the complete list of problems due on Friday.

There will also be a longer list of recommended problems, not to be handed in
You should be sure you can do them all and (even better) try some others from the text book as well.

The hand-in homeworks should be written up on 8.5 x 11 paper with "clean edges" (not torn out from a spiral bound notebook).  One goal in most upper level math courses is clear writing and arguments, so the solution of each problem should be written up quite clearly and legibly.  (In particular, check yourself by reading aloud the words and symbols you wrote down, exactly as written.  The result should be smooth sounding English--or else something is missing on paper!)


Talking with other students about homework problems is a good way to learn, but each student must write up his or her own homeworkTherefore, no solutions from two students should look too much alike.  After all, everybody says things in their own way, makes up their own notation as needed, etc.  A good way to avoid "copying" even inadvertently from another student is to talk about problems together without taking any notes away from the conversation.  This lets you share understanding and ideas, but forces you to reconstruct your own understanding on paper.

A grader will assign a score to each homework.  Each score will be rescaled to a %, and the lowest two scores will be dropped.  The average of the remaining %'s will be your homework score, H.


Homework Due Date
Problems to Hand In
Other Recommended Problems
(not to hand in)
Solutions to Hand-In Problems & Quizzes
Friday, September 7
Sec 1.1: 18,22,34

Sec 1.2:  12,14,20, 28, 30
Sec 1.1:  1,5,7,13,15,23,24,25,33

Sec 1.2:  3,13,15,21,22,23,29,31,
              33

Friday, September 14

Reminder: short quiz in class Friday 9/14
Sec 1.3: 12,14,18,
26,32

Sec 1.4:  8,14,18,20,
30,32

Sec 1.5:  6, 16, 28, 32

Sec 1.6:  12 (assume all the streets are one-way, so that traffic must flow in the indicated directions)
Sec 1.3: 5,7,9,23,24,25,27


Sec 1.4:  7,13,23,24,35

Sec 1.5:  13,23,24,31


Friday, September 21
Sec 1.7:  14,26,36,40


Sec 1.8:  6,10,26,32,34


Sec 1.9:  4,8,12,20,36

Section 1.10:  10
Sec 1.7: 1,15,17,19, 21,22,23,27

Sec 1.8:  3,13,15,18,21,22,
27

Sec 1.9: 13,19,23,24,27

Friday, September 28

Reminder: short quiz in class Friday 9/28.

Typically, material on a quiz will go up through the sections/material included in the homework due the same day.
Sect 2.1:  6,10,24,34

Sec 2.2:  6, 14, 22, 24, 30, 32, 38

Sec 2.3:  (Note the opening sentence for the exercise set:  "Unless otherwise
specified, ... "
)  2,4,8,14,18,34,38
Sec 2.1:  11,13,15,16,17,19,23,25

Sec 2.2: 3,9,10,12

Sec 2.3:  11,12,17,21,37



Friday, October 5
Reminder: 
Exam 1
in class on Monday October 8
Sec 2.6:  4
Sec 2.4:  4, 6 (in #6, assume that A ,C, X, and Z are square)

Sec 3.1:  8, 16 (see note in text preceding Problems 15-18) , 42

Sec 3.2:  8, 14, 22, 26, 34
Sec 3.1:  39,40

Sec 3.2:  15,17,19, 27,28, 33, 36

Friday, October 12


Sec 3.2:  36

Sec 3.3:  22,24,28,30

Sec 4.1:  2, 8, 20, 28, 30 (Hint: use #28)

Sec 3.2:  35

Sec 3.3: 29

Sec 4.1: 1,5,6,25,26,27


Since Friday, October 19 is Fall Break, the homework that would normally be due then will be collected on Monday, October 22.  I will try to have the complete assignment posted here by Monday,  October 15.


Sec 4.2:  6,12,14,22,32,34
( in #34, C[0,1] is the vector space of all continuous functions defined on the closed interval [0,1] )


Sec 4.3:  8,14,16,20,26,32 (#32 should also say "T is linear "), 34
Sec 4.2: 2,10,11,19,
25,26

Sec 4.3:  1,3,5,11,21,22, 29, 30,33

Friday, October 26

Quiz in Class Friday, October 26
Sec 4.4:  8,14,30,32

Supplementary Problems
based on the handout
Introduction to Diagonalization
Sec 4.4:  3,5,10,15,16

Friday, November 2
 
 

Sec 4.5:  6,12,14,16,22,24

Sec 4.6:  4,12,14,24

Sec 4.9:  4,14
Sec 4.5: 3,19,20,28

Sec 4.6: 17,18,27

Friday, November 9

(Quiz in class Friday November 9)
Sec 5.1: 8,16,20,24,36

Sec 5.2: 14,18,20,24  ("algebraic multiplicity" is what I called "multiplicity" in class;  sometimes the dimension of the eigenspace is called the "geometric multiplicity" of the eigenvalue.)

Sec 5.3:  4, 6, 8, 12 (The eigenvalues for #12 are given just before #7, at the bottom right corner of p. 325)
Sec 5.1:  1,3,7,21,22,35

Sec 5.2:  5,7,21,22,25

Sec 5.3:  3,21,22

 
 Friday, November 16


Sec 5.4:  4,10,16, 26 ( use 25 )

Sec 5.5:  6, 8,12,16
Sec 5.4:  3,15,25

Sec 5.5:  25

Friday, November 30
Quiz in Class Friday, December 7 (not November 30, as advertsied earlier)
Sec 5.6:  2, 6,10

Sec 6.1: 14,18,24,26,28

Sec 6.2: 10,14,16,20,22,28
Sec 5.6:  1,18 (if you have access to Matlab or a similar tool to assist)

Sec 6.1:  9,11,19,20,31

Sec 6.2:  1,5,23,24

Friday, December 7

Quiz in Class
Sec 6.3:  10,16,20,24
Sec 6.4:  4,8,12
Sec 6.5:  4,8,12,14,24
Sec 6.6:  4, 8a,10a,14
Sec 6.3: 5,21,22
Sec 6.4: 17,18
Sec 6.5: 17,18,25
Sec 6.6:  7, 9.  It's nice to do 8b and 10b if you can have Matlab or some other program help with the computations.



These problems are recommended for practice, but no more homework is to be handed in.

Sec 7.1: 10,12,15,19 (notice that the eigenvalues are given in the paragraph preceding Problem 13), 25,26,33,35

Sec 7.2: 3,5,7,11,13,19

Quizzes
In alternate weeks (unless there is a holiday or exam that week) there will be a short quiz, no more than 15 minutes, given toward the end of the class.  This means there will be about six quizzes during the semester.  The first will be on Friday,  September 14. These quizzes will contain one or more questions requiring you to do a very simple calculation, interpret a calculation, give a definition, state a theorem, or answer some true/false questions.  There will be no make-up quizzes  The quiz scores will be rescaled as a %, and the lowest score dropped.  The remaining scores will be averaged together to produce your quiz score, Q.
Tests 
There will be two exams (E1, E2) in class during the semester.  The dates of these exams will be announced at least 1 week in advance, but the dates will probably be in late September and late October.  
          After E2, there will be an optional Exam 3 (E3) given in the late afternoon or evening, probably in late November. 
          (See details under "Grading" below.)



          The final exam (F) will be held at the time scheduled in the Course Listings book:
Tuesday, December 18, 2007, 10:30-12:30 in the regular classroom, Cupples I, room 113
          Information about each exam will be posted in the table below when available.


Course Grade

        
Your grade will be based on T, your Total Score (%), computed as follows:

1) if you do not take the optional Exam 3:  T = (1/5) * (E1 + E2 + F + Q + H )
(so exams, quizzes and homework scores are all equally weighted)

2) if you do take the optional Exam 3, then your T will be the larger of

                         T = (2/11) * (E1 + E2 + F + Q + H) + (1/11) * E3

                         T = (2/12) * (E1 + E2 + E3 + F + Q + H )

(so if you choose to take E3, you have to take it seriously:  the score will count and it could hurt your Total T.  However if E3 doesn't go well, it will carry only half the weight of the other exams;  if it helps you, it will count the full weight of the other two exams.)
                    I  will base grades on the  number T, rounded up to the nearest integer.  I will not make up a grading scale until the end of the course, but it is guaranteed that the grading will be no more severe than:
90-100   A  (possibly +/-)
80-89     B  (possibly +/-)
65-79     C  (possibly +/-)
50-64     D
< 50      F
                     If you are taking the course on a CR/NCR (=pass/fail) basis, then you will need a T score value to a C- or better to earn a "CR"


Course Evaluations   Online Course Evaluations will be available toward the end of the semester.  I urge all of you to participate.  Thoughtful and accurate feedback is valuable to both the instructor and to your fellow students.


Academic Integrity  This link gives the general policies of the University on academic integrity.  Please also see the comments, above, about homework collaboration.


Anonymous Feedback to Professor Freiwald.  Of course, I'd really prefer open feedback and discussion about the course at any time.  However, this link is provided as a way for students to offer suggestions and comments anonymously.  I'll keep this link here as long as it's constructively used.
  (I can't respond, of course,  to your anonymous e-mail.)