Math 309,
Matrix Algebra
Fall 2011
Note:
In fall 2011, the Electrical & Systems Engineering Department
will teach E35 ESE 309 Matrix Algebra. ESE 309 has essentially
the same course description and, taken this fall, it will be
interchangeable with Math 309 for purposes of a mathematics major or
minor. The two courses may vary a bit in emphasis and selection
of some optional topics. ESE 309 has a smaller enrollment (about 30) and meets on a TuTh 12:30 schedule.
This
syllabus applies only to Math 309, not ESE 309
Instructor: Professor Ron Freiwald  Office Cupples I, room 203A, 9356737   Semester Office Hours Monday 34:30, Tuesday 34:30, Thursday 2:303:30 It
may be necessary occasionally to change office hours. In that
case, I will try to send an email in advance about the change. If
you find me in my office at other times, you are welcome to
ask whether I'm free for a question, or to make an appointment.
Extended Office Hours: Reading Period Week of December 12 (week before Final Exam) Monday, Tuesday: 35 Wednesday 23:45 ThursdayFriday 2:304
Distribution of scores from Exams 1, 2 and Final
Course Scores and Grades
 Lectures
 Brown Hall, Room 118 MWF
1112
a.m.

Course
Bulletin
Board This
box will be used to highlight announcements for the class.
The Bookstore might come up a little short on copies of det()the textbook.
Any shortage is due to a backlog of orders with the publisher
(not the Bookstore's fault). If you cannot purchase a book at the
bookstore (or elsewhere) at this time, contact me for a "fix" that will
last for a few weeks. (See link for text information.) 
Textbook & Related Resources, Homework, Exams/Dates, Course Grades
This link provides essential information, some of which (homework and
future exam dates) that you should read immediately.
____________________________________________________________________________________________________
Weekly Schedule, Assignments and Resources for Fall 2011 Past weeks are "grayed out"
Weekly Reading & Events

Monday 12/12 35 Tuesday 12/13 35 Wednesday 12/14 23:45 Thursday 12/15 2:304 Friday 2:304
I'm not sure, yet, about Monday, 12/19 WebWorK Assignments  Homework Hand
In

Other
Recommended
Problems (not to hand in)

Supplements & Solutions

Week of August 28
Be sure to read How to Study Linear Algebra at this link OR in your Study Guide.
Read Note to Students (preceding Chapter 1) in text
Read the Introductory Example (about Leontief) at the start of Chapter 1.
Read Sec 1.11.2 and 1.6; start on 1.3 (this will put you just a bit ahead of the lectures)
 WebWorK WW 1 is now open; see information listed under Homework
 There are handin HW problems you
can start on now.
See the list, below, for HW 1. Note HW 1 due in class Friday next week: September 9.  In every section, read the Practice Problems before starting the homework: for example, on p. 9 for Sec. 1.1
Notice that nearly every Section contains some "true/false" questions which are an excellent way to check your understanding. For example, 2324 in Sec. 1.1
Sec 1.1: 5, 7, 19, 23, 24, 25, 31
 PDF for Lecture1 (this version contains only examples, etc. not in test, has "normal" font size to save paper in printing, etc.)
PDF for Lecture 2
  WebWorK  Solve using the reduced matrix Hand
In  Problems (not to hand in) 
 Week of September 4 Monday: September 5: Labor Day: no class
HW 2: Due in class Friday, September 12
Sec. 1.4 Read Sec. 1.5 Read Sec. 1.6
Start reading Sec 1.7 (this will put you just a bit ahead of the lectures)  First WebWork Assignment WW1 due online by 11:59 p.m. Tuesday, September 6.
WW2 opens 12:01 a.m. Wednesday, September 7  HW1 due in class Friday, September 9.
Always include enough detail in every homework solution so the reader can understand how you got your answer.
Sec 1.1: 24, 26, 33, 34 Sec 1.2: 4,14,16, 30 (refer back to 29 for teminology) Sec 1.6: 8
Solutions for HW1

Sec 1.2: 7, 13, 19, 21, 22, 25, 31
 Example: Closed Exchange Economy (for Wednesday lecture)
PDF for Lecture 3
PDF for Lecture 4
_______________________
Some online tools that might be helpful for "small matrix" HW type problems (find others via Google, or pick the one you like):
Row Reducer
Row Echelon Form
Online Row Reducer
Be sure you can do row reductions by hand for small matricese.g., for exams.
  WebWorK  Hand
In  Problems (not to hand in) 
 Here are some additional problems (not to hand in) to help you study the rest of the material covered later next week.
Sec. 6.6: 1, 7 (part a), 8 (part a), 9, 10 (part a)Week of September 11
Read Sec. 1.5 Read Sec. 1.6 Read Sec. 1.7 Read Sec. 1.8
Wednesday, 9/14 is the last day to DROP a course.  WebWorK WW2 due online at 11:59 p.m. Tuesday, September 13.
WW3 opens 12:01 a.m. Wednesday, September 14.  HW2 due in class Friday, September 16
Always include enough detail in every homework solution so the reader can understand how you got your answer.
Sec 1.3: 12, 14, 16, 26
Sec 1.4: 6,16,18, 20, 22,30,34
Sec 1.5: 12, 18, 28, 30
Sec 1.7: 24, 28
Solutions for HW2

Sec 1.3: 7, 23, 24, 25, 32
Sec 1.4: 13, 17, 23, 24
Sec 1.5: 23, 24, 29, 31. 36
Sec 1.7: 18, 20 21,22
 PDF for Lecture 5
PDF for Lecture 6
Extra Example: Solution Sets of Linear Systems, Sec. 1.5: was in PDF for Lecture 6
PDF for Lecture 7
  WebWorK  Hand
In  Problems (not to hand in)

 Week of September 18
Read Sec. 1.8 Read Sec. 1.9 Read exmples on Diet and Difference Equations in Sec. 1.10
Engineers might like to also read the example on electrical networks.)
Read Section 2.1  WebWorK WW3 due online at 11:59 p.m. Tuesday, September 20.
WW4 opens 12:01 a.m. Wednesday, September 21.  HW3 due in class Friday, September 23
Always include enough detail in every homework solution so the reader can understand how you got your answer.
Sec 1.7: 32
Sec 1.8: 16, 18, 30
Sec 1.9: 4, 10, 12, 16, 20, 26, 27
Solutions for HW3

Sec 1.7: 29, 30,3338 (t/f)
Sec 1.8: 13, 15, 21, 22, 32
Sec 1.9: 13, 23, 34
 PDF for Lecture 8
PDF for Lecture 9
PDF for Lecture 10
Linear Difference Equation Example, Lecture 10
Applet illustrating linear transformations of the plane R^2
  WebWorK  Hand
In  Problems (not to hand in)   Week of September 25
Read Sec. 2.1 Read Sec. 2.2 Read Sec. 2.3  WebWorK WW4 due online at 11:59 p.m. Tuesday, September 27.
WW5 opens 12:01 a.m. Wednesday, September 28.  HW4 due in class Friday, September 30
Always include enough detail in every homework solution so the reader can understand how you got your answer.
Sec 1.10: 10
Sec. 2.1: 6, 8, 12, 22, 24, 28
Sec 2.2: 12, 16, 20
Solutions for HW4

Sec. 2.1: 13, 15, 16, 17, 20, 27
Sec 2.2: 9, 10, 13
 PDF for Lecture 11
PDF for Lecture 12
How Elementary Matrices Relate to Row Reduction (Lecture 12)
PDF for Lecture 13
  WebWorK  Hand
In  Problems (not to hand in)   Week of October 3
Read Sec 2.4 (only up to Theorem 10, p. 119)
Read handout/pdf notes about LU decompositions (available in right column by Monday, October 3).
Read Section 2.4, pp. 123137 (similar to the pdf notes) Engineers might like to read the last example in Section 2.5.
Read Section 2.6: I want you to be familiar with this, but I will not discuss iit in class. I will give you a written supplement.
Material in 2.8, 2.9 is intended by author to be skipped in a course that's going to do Chapter 4 (as we are).
Read Section 3.13.2  WebWorK WW5 due online at 11:59 p.m. Tuesday, October 4.
WW6 opens 12:01 a.m. Wednesday, October 5. but will not be due until Tuesday, October 18 at 11:59 pm.
Then WW7, as usual, will open at 12:01 am on Wednesday, October 19  HW5 due in class Friday, October 7
Always
include enough detail in every homework solution so the reader canSolve
using the reduced matrix understand how you got your answer.
Sec. 2.2: 22, 24, 32, 38 (For
problems in 2.2, try to answer using only material from 2.2 or earlier.
Don't say, "by the Invertible Matrix Theorem" which isn't stated until
Sec. 2.3)
Sec. 2.3: 6, 8, 14, 18, 22, 28, 36
Section: 2.4: 2, 6
Section 2.5: 4
Solutions for HW5

Sec 2.2: 21, 23
Sec. 2.3: 11, 12
 PDF for Lecture 14
Notes on LU Decomposition (distributed in class)
Practice Exams from the Textbook Author: may or may not be like ourexam, but good questions for practice.
PDF for Lecture 15
PDF for Lecture 16
  WebWorK  Hand
In  Problems (not to hand in)   Week of October 10
Inb Sec. 3.3, skip Cranmer's Rule and formula for inverse in therms of adjugate. But read "Determinants as Areas or Volumes"
Exam 1, in class Wednesday October 12
Information about Exam 1  No
WebWorK due this week: but WW 6 is open, and is due on Tuesday, October 18 at 11:59 pm.
There are a couple of LU decomposition problems in WW6 that you may want to practice before the
exam
 No regular HW due in class this week.
But part of HW 6 is Sec 2.5: 24 Sec 2.6: 6 Sec. 3.1: 14, 16
For
HW 6 (due on Friday, October 21): this list will grow longer than usual
since HW 6 spans a larger set of lectures. So don't put it all
off.

 PDF for Lecture 17
Solutions for Exam 1
Distribution of Scores on Exam 1
Solutions for Exam 1 will be posted here late afternoon Monday October 17.
  WebWorK  Hand
In  Problems (not to hand in)   Week of October 17
Finish the reading assigned in Section 3.3.
Read Sections 4.1, 4.2
Exam
1 was available for pickup in class Wednesday; I will bring them again
Friday. After that, they will need to be picked up at my office,  WebWorK WW6 due online at 11:59 p.m. Tuesday, Oct.18.
WW7 opens at 12:01 am on Wednesday, October 19. WW7 contains a few review problems, and is a bit shorter than usual.
Note: WW7 uses the notation R^(nxn) for the vector space of n x n matrices

HW 6 due in class on Friday, October 21
Always include enough detail in every homework solution so the reader can understand how you got your answer.
Sec 2.5: 24 Sec 2.6: 6 Sec. 3.1: 14, 16 Sec. 3.2: 8, 24, 30, 34, 35 Sec, 3.3: 22, 24, 28, 30
Solutions for HW6

Sec. 3.1: 39, 40 Sec, 3.2: 16, 18, 20, 27, 36 Sec 3.3: 27,29
 PDF for Lecture 18
PDF for Lecture 19
Supplementary Examples of Vector Spaces and Subspaces
PDF for Lecture 20
  WebWorK  Hand
In  Problems (not to hand in)   Week of October 24
Read Sec 4.3, 4.4,  WebWorK WW7 due online at 11:59 p.m. Tuesday, October 25
Note: WW7 uses the notation R^(nxn) for the vector space of n x n matrices
WW8 opens at 12:01 am on Wednesday, October 26.
 HW 7 due in class on Friday, October 28
Always include enough detail in every homework solution so the reader can understand how you got your answer.
Sec. 4.1: 8, 18, 22, 28, 32
Sec. 4.2: 12, 14, 24, 28, 32, 33
Sec 4.3: 4, 10, 12, 24
Solutions for HW7 
Sec 4.1: 2, 3, 23, 24
Sec. 4.2: 17, 20, 25, 26
Sec. 4.3: 21, 22, 23  PDF for Lecture 21
PDF for Lecture 22
PDF for Lecture 23
Supplementary examples on rotation of axes (from Friday's lecture)
  WebWorK  Hand
In  Problems (not to hand in)   Week of October 24
Be sure you've read through Section 4.4 and the example on rotation of axes (last Friday's lecture)
Read the notes on Introduction to Diagonalization and the Extra Example distributed in class. You will need this material for the last part of HW 8.
The material is related to Sections 5.1  5.3 in the text. If you like, you can read ahead in Section 5.1
Read Sections 4.5 and 4.6
Exam 2 next week (see below)
Information about Exam 2
 WebWorK WW8 due online at 11:59 p.m. Tuesday, November 1.
Because of Exam 2 next week, no WebWorK due next week
WW9 will open at 12:01 am Wednesday, November 2, but will not be due until 11:59 pm Tuesday, November 15.
 HW 8 due in class on Friday, November 4
Always include enough detail in every homework solution so the reader can understand how you got your answer
Sec. 4.4: 8, 12, 14, 22, 32
Do this supplementary problem on rotation of axes
Do these supplementary problems on disgonalization
HW8 Solutions 
Sec. 4.4: 1, 5,10, 15, 16  PDF for Lecture 24
Notes: Introduction to Diagonalization (Monday's lecture)
Extra Example on Diagonaliazation
PDF for Lecture 25
PDF for Lecture 26
Example: A Markov Process and its Relation to Diagonalization
  WebWorK  Hand
In  Problems (not to hand in)   Week of November 7
Skip Section 4.74.8
Read Section 4.9 (and the example from class (last week) about Markov Processes.
Read Sec 5.15.3
Exam 2, in class Wednesday, November 9
For Friday: please also read this note Where are we in relation to the textbook?
 Because of Exam 2 on Wednesday, no WebWorK due this week. WW9 will be due on Tuesday, Nov. 15  No regular HW due in class this week.
HW9 will be due in class on Friday, Nov. 18. But parts of HW 9 will be posted here this week so you can get started.
HW 9:
Sec. 4.5: 6, 8, 14, 22, 31
Sec. 4.9: 4, 8, 14 
Sec. 4.5: 19, 20, 29, 30  PDF for Lecture 27
Example: Eigenvalues, Eigenvectors and Eigenspaces (Friday Lecture)
Exam 2 Solutions
Score distributions for Exams 1 and 2
  WebWorK  Hand
In  Problems (not to hand in)   Week of November 14
Read Section 5.4 and be sure you've read the introductory example for Chapter 5 on spotted owl populations: I will idscuss on Friday.
Start reading Section 6.1
Friday, November 18: last day to withdraw from course without recommendation from Student Health Services  WebWorK WW9 due online at 11:59 p.m. on Tuesday, Nov. 15
WebWorK WW10 opens at 12:01 a.m. on Wednesday, November 16.
It is due online at 11:59 p.m.on Tuesday, November 29 (the Tuesday after Thanksgiving break).
Because
of the break. WW10 is somewhat shorter (9 problems), and you
should know everything you need for WW9 after Wednesday's lecture. You
should be able to finish the assignment befor Thanksgiving break if you
want to.  HW 9: due in class on Friday, Nov. 18.
Always include enough detail in every homework solution so the reader can understand how you got your answer.
Sec. 4.5: 6, 8, 14, 22, 31
Sec. 4.9: 4, 8, 14
Sec 5.1: 14, 27, 35
Sec. 5.2: 16, 18
Sec. 5.3: 6, 14, 16, 24
Solutions for HW9 
Sec. 5.1: 21, 22
Sec. 5.2: 21, 22
Sec 5.3: 21, 22  PDF for Lecture 29 (this contains a fuller outline of Monday's lecture than is usually posted here)
Supplement: Proofs for the theorems about diagonalization
PDF for LectuSolutions for HW9re 30
Extra Example related to Wednesday's Lecture: Bmatrix for a linear transformation
PDF for Lecture 31
Examples: Spotted Owls and Wood Rats
  WebWorK  Hand
In  Problems (not to hand in)   Week of November 21
If you haven't already done so, be sure to read the material about Spotted Owls on pp. 265266.
Read part of Section 5.6: pp. 301303, and the Spotted Owl material pp. 307309 The other material in the Section is nice but optional.
Read Section 6.1
November 2327 Thanksgiving Break so no class Wednesday or Friday  WW10 due at 11:59 p.m. on Tuesday, November 29.
No WebWorK due this week, but the due date is just two days after Thanksgiving Break  so try to finish before Break!
 No written HW due this week. HW 10 will be due in class on Friday, December 2.
Some of the HW 10 problems are posted here in case you want to work on them
For HW 10:
Sec 5.4: 4, 8, 14, 17, 22, 23
Sec. 5.6: 2 (find a "solution" means find a expression for xk in terms of the eigenvectors), 4, 5
Assignment will be complete before 5 pm Tuesday.

Sec 5.4: 10, 20
Sec.5.6: 1, 6
 PDF for Lecture 32
  WebWorK  Hand
In  Problems (not to hand in)   Week of November 28
Read Sections 6.16.4  WW10 due at 11:59 p.m. on Tuesday, November 29.
WW11 will open at 12:01 am on Wednesday, November 30 and be due at 11:59 pm on Tuesday, December 6.
WW11 is the last WebWorK assignment for the semester.  HW 10: due in class on Friday, December 2.
Always include enough detail in every homework solution so the reader can understand how you got your answer.
Sec 5.4: 4, 8, 14, 17, 22, 23
Sec. 5.6: 2 (find a "solution" means find a expression for xk in terms of the eigenvectors), 4, 5
Sec 6.1: 24,26
Sec. 6.2: 14,16, 28, 32, 34
The problem list for HW 10 is now complete.
Solutions for HW10

Sec 5.4: 10, 20
Sec.5.6: 1, 6
Sec. 6.1: 19, 20, 28
Sec. 6.2: 15, 26, 29  PDF for Lecture 33
Example: Orthogonal Bases and Projections
PDF for Lecture 34
Example: Using the Orthogonal Decomposition Theorem and Best Approximation Theorem
Example: 2x2 Orthogonal Matrices
PDF for Lecture 35
Notes and Example: the Gram Schmidt Process
  WebWorK  Hand
In  Problems (not to hand in)   Week of December 5
Finish reading Section 6.4 (You can skip the material
on QR Factorization: it's a nice topic and very good reading to see how
well you understand GramSchmidt Process but we won't have time to make any use of these QR factorizations.)
Read Sections 6.5 and 6.6
Friday, December 9: last day of class  WW11 is due at 11:59 pm on Tuesday, December 6.
This is the last WebWorK assignment for the course.
 HW 11: due in class on Friday, December 9
Always include enough detail in every homework solution so the reader can understand how you got your answer.
Sec. 6.3: 10, 18, 24, and an extra problem not in textbook (download from this link)
Sec. 6.4: 6, 19, 20 (note: although the letters Q, R are involved, you don't need to know anything about the "QR factorization"
Sec. 6.5: 4, 6, 12 (note: orthogonal columns!), 14, 24, 25
Solutions for HW 11

Sec. 6.4: 17, 18
Sec. 6.5: 17  PDF for Lecture 36
Example: least squares solutions for Ax = b
PDF for Lecture 37
Example: least squares and simple linear regression
PDF for Lecture 38
Inner Product Spaces  Week of December 12
Reading Period and Start of Final Exam Period  I created a set of 5 WebWorK problems related to least squares (Section 6.6): the set is called "LSPractice"
These problems are only for your practice: the "points" will not be part of your WW score for the course.  Here are some additional problems (not to hand in) to help you study the rest of the material covered later next week.
Sec. 6.6: 1, 7 (part a), 8 (part a), 9, 10 (part a)    FINAL EXAM Tuesday,
December 20, 2011, 10:3012:30 in the regular classroom: Brown 118
Final
Exam is 2 hours. Same rules and style as earlier exams. The final
exam will be based on the material starting with Chapter 4 (and earlier material only as needed for the later material)     
Academic
Integrity This link gives the general policies of the
University on academic integrity. Please also see the
comments about homework collaboration (above).
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 email.) 