Math 309, Matrix Algebra
Announcements, Weekly Reading and Homework
Fall 2015

NOTE THAT THIS IS AN OLD SYLLABUS: FALL 2015


                                                                    Course Announcements

Please check the course exam schedule so you can plan to avoid conflicts.

Always include enough detail in every written homework solution so the reader can see how you got your answer. 

The problems assigned below for written HW each week may be modified up until 5 p.m. Tuesday in the week that they are due.  Please (re)check the assigned problems each week after that time.


Weekly Reading & Events
WebWorK
Assignments
Written Homework
(to hand in)
Recommended
(not to hand in)
Supplements &
Solutions
 
Week of 8/24/15

Lectures 1-3

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. 1.1--1.3, and 1.6;  
WebWorK

WW 1 opens at 12:01 a.m. on Wednesday, 8/26. Your answers due online by 11:59 p.m. on Tuesday, 9/1.

See
 WebWork
for more details

Contact me right away if your name does not appear in WebWorK; include your name, WU ID number, and email address and I will add you into WebWorK's list.


You should get started quickly on the hand-in HW 1 problems. The HW1 set isn't due until Sept. 4m because I didn't want to collect HW on the first Friday.  But that means that HW1 will cover 2 weeks of work, and therefore will be longer than usual,

The problems for HW1 are listed in the week of 8/31, below, because that's the week in which they're due. 

See Homework for my guidelines about written solutions. The article 
Guidelines for Good Mathematical Writing might also be helpful now and in the future.

 
At the end of each section, try the Practice Problems before starting the homework: for example, on p. 9 for Sec. 1.1

Almost every section in the text contains some "true/false" questions. T
/F questions are an
excellent way to check your understanding.For example, 23-24 in Sec. 1.1

Sec 1.1: 5, 7, 11, 17, 19, 23, 24, 25, 31

Sec 1.2: 7, 13, 15, 19, 21, 23, 25, 31
Whenever you think you've spotted an error in one of these files, check with with a few other students and then, if necessary, let me know so I can repair if necessary.

PDFs for Lecture 1

PDFs for Lecture 2

PDFs for Lecture 3

One of the following might be useful for row operations

Row Reducer

Row Reducer App

Row Echelon Form

Wolfram Alpha

For those who use Matlab


WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 8/31/15

Lectures 4-6
 
Read Sections 1.4, 1.5, and 1.7


EXTENDED: WebWork Assignment WW1 due online by 11:59 p.m. WEDNESDAY, 9/2.

WW2 opens 12:01 a.m. Wed. 9/2




HW1 due in class Friday, Sept. 4

More problems may be added to this assignment up until Tuesday Sept 1., at 8 p.m.

Always include enough detail so a grader can see how you got your answer.

Sec. 1.1: 16, 22, 28, 33, 34

Sec. 1.2: 14, 16, 23, 24, 26, 28, 29, 30

Sec 1.3: 10, 12, 14, 20, 22, 26

Sec 1.6: 6, 12 (note that the figure is at the end of problem 12)

Sec. 1.4:  18, 26, 28, 34


Solutions for HW1

Sec 1.3: 7, 17, 19, 23, 24, 25, 31 (see 29 fpor teminology),32

Sec 1,4: 13, 17, 23, 24, 29

Sec 1.5:  23, 24, 29, 31, 34

Sec 1.6:  11 (There is an error in the picture in the textbook: flow should be 80 into
node C.
)











PDFs for Lecture 4

Supplement: Chemical Reaction from Two Points of View

Supplement: Economics: a simple closed economy

PDFs for Lecture 5

PDFs for Lecture 6
   WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 9/7/15

Monday, Sept. 7
LABOR DAY
NO CLASS
Lectures 7-8

Read Sections 1.7, 1.8


WebWork
Assignment WW2
due online by 11:59 p.m.Tuesday, 9/8


WW 3 will open at 12:01 a.m. on Wednesday, 9/9
HW2 due in class Friday, Sept. 11

Sec. 1.4: 32,36

Sec. 1.5: 8. 12, 18, 22, 30, 34, 36

Sec. 1.7: 2, 10, 16, 18, 20, 24

More problems may be added to this assignment up until Tuesday at 8 p.m.

Solutions for HW2
Sec. 1.5: 23, 24

Sec. 1.7: 3, 11, 21, 22
PDFs for Lecture 7

PDFs for Lecture 8
WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 9/14/15
 
Lectures 9-11

Read Section 1.9, 1.10, the introductory example for Chapter 2, and start reading Sectgion 2.1.

NOTE: in Section 1.10, you can skip the example on electirical networks. But those interested in physics and engineering should certainly read it.

 
Read the supplement
(right column) titled "A Linear Difference Equation" -- discussed in class
WebWork Assignment WW3
due online by 11:59 p.m.Thursday, 9/17 (an extended deadline this week)

WW 4 will open at 12:01 a.m. on Wednesday, 9/16
HW3 due in class
Friday, September 18

Sec.1.7: 28, 32, 36

Sec.1.8: 10, 12, 14, 16, 18, 20, 26, 32, 34

Sec.1.9:  4, 8, 10, 12, 14, 20, 30

Sec. 1.10: 10

Solutions for HW3

Sec. 1.7: 27, 29

Sec. 1.8: 3, 7, 9, 21, 22, 25

Sec. 1.9: 15, 21, 23, 24, 39, 35


PDFs for Lecture 9

Rotation Cartoon: is the matrix correct?

PDFs for Lecture 10

PDFs for Lecture 11

An example related to Sec. 1.10: A Linear Difference Equation
WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 9/21/15

Lectures 12-14

Read Sections 2.1 - 2.3; start Section 2.4
WebWork Assignment WW4
due online by 11:59 p.m.Tuesday, 9/22

WW 5 will open at 12:01 a.m. on Wednesday, 9/23
Homework 4 due in class Friday, September 25

Sec. 2.1: 4, 6, 10, 18, 22, 34

Sec. 2.2: 4, 14, 16, 20, 22, 24, 30, 32

Solutions for HW4


Sec. 2.1:  11, 15, 16, 20, 21, 24

Sec. 2.2:  9, 10, 17, 31
PDFs for Lecture 12

PDFs for Lecture 13

EROs and Multiplication by Elementary Matrices

PDFs for Lecture 14

Invertible Matrix Theorem and Connections to Previous Work

Left and Right Inverses to a Matrix Optional
WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 9/28/15

Lectures 15-17

Read Sections
2.4 - 2.5 (you can skip the factorization example in electircal engineering, except that if you're in EE syou should want to read it.

WebWork Assignment WW5 due online by
11:59 p.m.  Thursday, 10/1 (an extended deadline this week)

WW6 will open at 12:01 a.m. on Wednesday, 9/30. Because of  Exam 1 next week, WW6 will  be open for for 2 weeks: due by 11:59 p.m. on Tuesday, October 13. However, you should do Problems 1-4 as part of your test preparation.
HW 5, due in class on Friday, October 2.

Sec. 2.3: 6, 8, 14, 16, 18, 26, 
(assume A is square  --otherwise not true!), 34,38

Sec. 2.4:  4, 8 (assume A is square), 10 (find X,Y,Z, in terms of A,B, C)

Sec 2.5: 2, 6, 10, 17

Solutions for HW5
Sec. 2.3: 11, 12, 15, 23, 27  (assume A, B are square) )

Sec. 2.4:  1, 7

Sec 2.5: 1, 3, 15
PDFs for Lecture 15

PDFs for Lecture 16
This is a set of notes on Section 2.5.  I think they improve the exposition that's in the textbook. You are responsible for the material in the notes down to where the material marked OPTIONAL begins (about half way through)

PDFs for Lecture 17 (Leontieff Notes)

2 pages from Leontieff's Scientific American article (1965)
WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 10/5/15
Lectures 18-20

Read Sections 2.6 (and notes fposted from last Frida), 3.1, 3.2

Preliminary Information about Exam 1

Link for Practice Exam 1 (use Math 309 Exam from FL2012)


List of terms to know for Exam 1

Wednesday Oct 7
Exam 1, 7-9 p.m.
in Lab Sciences 300

Solutions for
Exam 1

WebWork Assignment WW6 due online by 11:59 p.m.Tuesday 10/13 (an extended deadline because of the exam: no WW due this week/

HW 6, due in class Friday, October 9
(shorter than usual because of the exam)

Sec 2.6:  6

Sec. 3.1:  6
(twice: once expanding across row 1, a second time going down col 2),  
14, 20, 22

Solutions for HW6
Sec. 2.6:  5, 7

Sec. 3.1: 3, 11, 14



PDFs for Lecture 18

PDFs for Lecture 19

PDFs for Lecture 20

Handout: A Linearity Property of Determinants
WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 10/12/15
Lectures 21-22

Read the part of Section 3.3 from p. 182-186 (you can skip the earlier pages).
Read also the pdf posted on A linearity Property of Determinants (also in text reading)

Read 4.1, and start reading 4.2

Exam Scores (part I) are in Blackboard.  You can also go to the Math Department
Score Lookup
page to see which questions you missed.

Lectures 21-22


Friday, October16
FALL BREAK
NO CLASS
WebWork Assignment WW6 due online by 11:59 p.m.Tuesday, 10/13

WW 7 will open at 12:01 a.m. on Wednesday, 10/14
HW 7:  There will be no homework due this week because of Fall Break.  But there are some problems posted here as part of the assignment that will be due in class on Friday, October 23.

Sec. 3.2: 12, 18, 20, 26, 32, 40

Sec. 3.3:  22, 28, 30, 32

Sec. 4.1:  8, 10, 12, 18, 20, 22, 28, 32

More problems may be added to this assignment up until Tuesday, October 20,  at 8 p.m.

Sec. 3.2:  27, 28, 35

Sec. 3.3:  29

Sec. 4.1:  3, 17, 23, 24
PDFs for Lecture 21

Handout: A Linearity Property of Determinants

PDFs for Lecture 22

WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 10/19/15
Lectures 23-25

Read Sections 4.2-4.3 and start reading 4.4


WebWork Assignment WW8 due online by 11:59 p.m.Tuesday, 10/20


WW 8 will open at 12:01 a.m. on Wednesday, 10/21
See (above) the problems for HW 7 that were assigned last week. They are part of the HW 7 assignment that is due on Friday, October 23

Sec, 4.2: 12, 14, 16, 28, 32

Sec. 4.3: 4,10

More problems may be added to this assignment up until Tuesday, October 20,  at 8 p.m

Solutions for HW7

Sec. 4.2:   23, 24, 25, 26, 33PDFs for Lecture 23

PDFs for Lecture 24

PDFs for Lecture 25
WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 10/26/15

Read Sections 4.4-4.6

Lectures 26-28
WebWork Assignment WW8 due online by 11:59 p.m.Tuesday, 10/27

No new WW opens this week because of Exam 2 next week.  

The next WW assignment, WW 9 will open no later than 12:01 a.m. Wednesday, 11/4 (perhaps earlier),  and be due by 11:59 p.m. Tuesday, 11/10.

HW8: Due in class Friday, October 30

Sec. 4.3:  16, 20, 26, 30, 34

Sec. 4.4: 4, 8, 14, 28, 32

Sec. 4.5: 4, 6, 8, 14

More problems may be added to this assignment up until Tuesday at 8 p.m.

Solutions for HW8
Sec. 4.3: 21, 22, 23, 34

Sec. 4.4:  15, 16

Sec. 4.5:  9, 19, 20, 29, 30
PDFs for Lecture 26

Supplement on
Rotation of Axes


PDFs for Lecture 27 (includes extra example on changing bases)

PDFs for Lecture 28

Handout on the Four Fundamental Subspaces
WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 11/2/15
Lectures 29-31
Read the notes (right column) for last Friday and Monday on the 4 fundamental subspaces, and on diagonalization; read Sections 5.1 - 5.2

Preliminary Information about Exam 2

Link for Practice Exam 2 (use Math 309 Exam 2 from FL2012)

List of some terms to know for Exam 2

Wednesday Nov 4
Exam 2, 7-9 p.m.
in Lab Sciences 300

Solutions for Exam 2
No WW assignment is due this week.

WW 9 will be open by 12:01 a.m.  Wednesday, 11/4, and will be due online by 11:59 p.m. Tuesday, 11/10.

WW 10 will open at 12:01 a.m. on Wednesday, 11/11.
HW 9: Due in class Friday, November 6 (shorter than usual because of the exam)

Sec. 4.6:  4, 8, 14, 16, 22, 24, 26

(No more problems to be added this week)

Solutions for HW9





Sec. 4.6: 3, 17, 18, 21The very few pdfs for Lecture 29 are contained within these notes: 
Introduction to Diagonalization

No PDFs for Lecture 30

PDFs for Lecture 31: Diagonalization examples

WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 11/9
Lectures 32-34
Read Sections 5.3-5.4

You can skip 5.5

Read Sec. 5.6:  focus on the predator-prey example and the spotted owls example.  For background, be sure to read the intorductory application for Chapter 5 on pp. 267-268..

Start reading Section 6.1.
WW 9 is due online by 11:59 p.m. Tuesday, 11/10.

WW 10 will open at 12:01 a.m. on Wednesday, 11/11
HW 10: Due in class Friday, November 13

Sec. 5.1: 12, 16,  20, 26, 27, 32

Sec 5.2: 4, 14, 18, 19

Sec 5.3:  4, 6, 12 (note that the eigenvalues for 12 are given in the paragraph preceding #7) ,20, 24, 26, 27, 32

Solutions for HW10
Sec. 5.1:  22, 23, 35

Sec. 5.2:  19, 21, 22

Sec. 5.3: 16, 21, 22,  27
PDFs for Lecture 32

Supplementary proofs about diagonalization



PDFs for Lecture 33

PDFs for Lecture 34

Supplementary material: Diagonalization and Fibonacci numbers
WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 11/16/15
Lectures 35-37

Read Sections 6.1-6.2 and start on 6.3

WW10 is due online by 11:59 p.m. on Tuesday, 11/17.

WW 11 will open at 12:01 a.m. on Wednesday, 11/18
HW 11: Due in class Friday, November 20

Sec. 5.4: 2, 4, 6, 10, 18

Sec. 5.6: 4, 6

Sec. 6.1:  10, 14, 24, 28

Sec. 6.2:  10, 14, 16, 22,  28, 34


Solutions for HW11
Sec. 5.4:  9, 23

Sec. 6.1: 19, 20, 25

Sec. 6.2:  13, 15, 23, 24, 27
PDFs for Lecture 35


PDFs for Lecture 36


PDFs for Lecture 37
WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 11/23/15
Lectures 38

Read Sections 6.3-6.4 (you can skip the QR-Factorization section if you like--it does come up a lot in engineering applications) and the handout (in class, & online) about the Gram-Schmidt Process.


Wed-Fri Nov 25/27
THANKSGIVING 
BREAK: NO CLASS

Have a nice Thanksgiving Holiday!
WW11 is due online by 11:59 p.m. on Tuesday, 11/24.

WW12 will open at 12:01 a.m. on Wednesday, 11/25, but it will not be due until 11:59 p.m. on Friday, 12/4 (the last day of class)


HW12 will be due in class on Friday, 12/4 (the last day of class)

The HW12 problems are all listed together in next wek's section of the table.



Sec. 6.3:  21, 22, 23

Sec. 6.4: 17,18

PDFs for Lecture 38

Handout on the Gram-Schmidt Process


WebWorKWritten Homework Hand InRecommended
(not to hand in)
Supplements &
Solutions
Week of 11/30/15

Be sure to read the introductory example for Chapter 6 (pp. 331-332) and a good motivation for Sections 6.5-6.6

Read Sec 6.5 stopping at the end of Example 4), and Sec. 6.6

Lectures 39-41

WW12 is due online by 11:59 p.m. on Friday, 12/4.

The problems for HW 12 (including those on last week's topics) are all listed here since they are not due until Friday,12/4.

Sec. 6.3:  6. 10, 14, 18, 20, 24

Sec. 6.4: 6,12, 20 (although the problem contains the letters Q and R, you do not need to know anything about QR factorizations.)


Sec, 6.5:  4, 8, 10, 14, 20, 25

Sec. 6.6: 4,  8 (part a) only), 10 (part a) only)


PDF file containing  Problem 25 from Sec. 6.5 (missing in some online textbooks)

Solutions for HW12

Sec. 6.5: 17, 18

Sec. 6.6: 5, 9
PDFs for Lecture 39

PDFs for Lecture 40

PDFs for Lecture 41

Some notes and example about innerproduct spaces (optional supplement related to unnassigned material in 6.7)
FINAL EXAM, THURSDAY MORNING

Chapters 4-6
No hand-graded part

Link for Practice Exams (use Math 309 Exam from FL2012)

Information about the final exam
Dec. 108-10 a.m.Lab Sciences 300