Linear Algebra 2270-4 Spring 2019

Math 2270-4	Linear Algebra, Spring 2019
Instructor	G.B. Gustafson, PDF Syllabus Here, HTML Syllabus Here
Office hours	JWB 113 after class, and by appointment. (801) 581-6879 Email preferred. Office Hours: Door Card Hours and Email Address.
Lecture	Linear Algebra 2270-4 meets at 12:55pm MTWF in JFB-102. Computer Lab in LCB 115 on select Tuesdays, 1:45pm. Information about Problem sessions Here.
Midterm Exams	Exams held from 12:50pm to 1:50pm on Friday 15 Feb, Friday 29 Mar, Friday 12 Apr.
Final Exam	Exam 1:00pm to 3:00pm on Tuesday 30 April, regular classroom.
Textbook	David C. Lay, Linear Algebra and Its Applications, 5E (2015). Book Cover Here The default eBook includes Pearson MyLab, integrated with CANVAS.
Online Grades	Web site for Utah Canvas

Last change: Tuesday May 07: 19:57PM, 2019

Course Calendar Weeks 1-6

First Week	First exercise package Here is due on Friday of Week 1 [11 Jan]. First Day Info Here, distributed first day of class. Course content, First Day Lecture Here The default is an online textbook. If you require a printed book and the bookstore has no 2270 textbooks, then get the first chapter here: Chapter 1 Instructions from Pearson for using the eBook Here The Math Center in the basement of building LCB is open with study areas, computers and free tutoring: Read this memo for details. Course Web page access to all files: Directory Here
Reading	Background: Read Linear Equations no matrices A major goal of the course is to be able to read and understand Gilbert Strang's article The Fundamental Theorem of Linear Algebra. The free 1993 jstor PDF is available via the Marriott library. Requires UofU 2-factor login.
Jan 7-11	Week 1: §1.1 Systems of Linear Equations, §1.2 Row Reduction and Echelon Forms, §1.3 Vector Equations. Friday HW: Here, one problem. Chapter 1 slides Here Fundamental Theorem on Tookit Sequences is Theorem 11, page 326, with proof on page number 334 [19th page] of reference matrix-eqn.pdf
Jan 14-18	Week 2: §1.4 The Matrix Equation A x = b , §1.5 Solution Sets of Linear Systems. Friday HW: Here. Chapter 1 slides Here
Mon Jan 21	Martin Luther King Day, no university classes on Monday
Jan 21-25	Week 3: §1.6 Applications of Linear System, Chemical Balance Example PDF here §1.7 Linear Independence, §1.8 Introduction to Linear Transformations. Friday HW: Here
Jan 28 to Feb 1	Week 4: §1.9 The Matrix of a Linear Transformation, Coordinates, Differential Geometry background §1.10 Optional Linear Models in Business, Science, and Engineering, §2.1 Matrix operations, §3.1 Determinants (Exercises 15-18, Sarrus' Rule), §2.2 The Inverse of a Matrix. §2.3 Characterizations of Invertible Matrices. Friday HW: Here. Chapter 2 slides Here Project Deadline Feb 2: Create or join a semester project group by email. Some topics and sample projects can be found on the Projects Page.
Tue Jan 29	Lab 1: Intro to Maple, Meet in computer lab LCB 115, 1:45pm. Due by Mar 1. Maple Setup with photos and Lab 1 examples Utah Maple Web Help 2019 Here. Maple, Matlab, MuPad setup and remote login help is available in the maple sources Directory.
Feb 1	Semester Project Deadline Feb 1: Create or join a project group. Email to Dr G your Title, Group Members, Abstract, Contact email addresses. Sample email text for the Feb 1 deadline: Click Here Please communicate edits/changes by email to Dr G until the last day of classes. Presentations of projects on April 22 and 23. The project is submitted by email, deadline midnight May 7.
Tue Feb 5	Lab 2: Traffic Flow. Meet in computer lab LCB 115, 1:45pm. Due by Mar 1.
Feb 4-8	Week 5: §2.4 Partitioned Matrices, §2.5 Matrix Factorizations, §3.1 Introduction to determinants. Continued from Week 4. §2.6 Optional The Leontief Input–Output Model, §2.7 Optional Applications to Computer Graphics, §2.8 Subspaces of R^n, Delayed. §2.9 Dimension and Rank, Delayed. Missed the Project Deadline? Create or join a group by Feb 2. Use email. YouTube video on LU-decomposition Chemical Balance example from 1.6 PDF: maple shortcuts LU-Decomposition MAPLE DEMO from Friday 8 Feb TEXT: maple text and PDF: Output from the computation Chapter 2 slides Here (Determinants, PIVOT Theorem, Fund Thm Toolkit Sequences) Friday HW: Here ONE WEEK WARNING: Exam 1 is Friday February 15, 12:50pm to 1:50pm. Sample Exam 1 on Chapters 1 to 3 for S2019: Questions and Answers(some topics removed due to Feb 6 snow day) Old Midterms from S2018, covers all 3 exams in S2019: Questions and Answers 2018 Exam 1 Problems 1,2,3,4,5,6(b) apply to 2019. Skip 6(a),6(c). The 2019 exam is shorter in solution time due to the 1-hour time limit. Questions and Answers 2018 Exam 2 Exam 1 Review, 4:30-6pm LCB 215 Thursday February 7, Blackboard photo directory (see topics removed due to snow day Feb 6) Snow day delay: Friday HW due this week is delayed until Monday Feb 11.
Feb 11-15	Week 6: §3.2 Properties of determinants, continued, §3.3 Cramer’s rule, volume and linear transformations, Summary of delayed section §2.8 Subspaces of R^n, §4.1 Vector spaces and subspaces. Maple example for Cramer's Rule HERE (cramers-rule-example.pdf) Subspace examples discussed in class HERE (includes slot car racer and least squares). Semester Project Abstracts 2019 are found HERE (updated 10 Feb) Friday HW: Here. This HW is NOT due this week: it is delayed until Tuesday Feb 19. Chapter 3 slides Here, Chapter 4 slides Here Maple from home, UofU Library Remote Maple 2017 How To Use It EXAM 1: 12:50-1:50pm Friday February 15 Link to Typeset Solutions to 2019 Midterm 1 (uploaded 19 Feb 2019) Link to Student Solutions to 2019 Midterm 1 (uploaded 19 Feb 2019) Project ABSTRACTS Click Here Please read and update your abstract and title. Email addresses exist for each group. To make contact or join a group, please send me email. The REPLY will contain the email addresses.

Course Calendar Weeks 7-13

Mon Feb 18	President's Day, no university classes
Tue Feb 19	Lab 3: Adjacency Matrices and Airline routes. Meet in computer lab LCB 115, 1:45pm. Due by Mar 29. Data sources written in Maple for Lab 3 are located in this Directory Maple from home, UofU Library Remote Maple 2017 How To Use It
Feb 18-22	Week 7: No class Monday: President's Day holiday §4.2 Null spaces, column spaces, and linear transformations, Summary of delayed section §2.9 Dimension and Rank, §4.3 Linearly independent sets and bases. Friday HW: Here. Chapter 2 Slides, Chapter 3 Slides, Chapter 4 Slides
Feb 25-28, Mar 1	Week 8: §4.4 Coordinate Systems, §4.5 The dimension of a vector space, §4.6 Rank. Notes on coordinates and change of basis located in this DIRECTORY, file coordinates.pdf Maple demo on powers of stochastic matrices:Example 3, Section 4.9 Friday HW: Here Due Friday March 1, postponed to Monday March 4. Due today March 1: Maple Labs 1 and 2. Tuesday Feb 26: Lab 3: Adjacency Matrices and Airline routes. Makeup session. Meet in computer lab LCB 115 at 1:50pm. Due by Mar 29. Data sources written in Maple for Lab 3 are located in this Directory
Mar 4-8	Week 9: §4.7 Change of basis, §4.8 optional, Applications to Difference Equations, §4.9 optional, Applications to Markov chains, Google search algorithm and Markov Chains: Perron-Frobenius Theorem, Chapter 10 online at PearsonHigherEd.com, §5.1 Eigenvectors and eigenvalues, Appendix B: Review of complex numbers. Applications of eigenvectors and eigenvalues, answer to question March 5, 2019 PDF document Chapter 5 Slides: Here, Friday HW: due March 8. Here Project Deadline: Group leader submits project draft by Mar 11. Final copy due by Midnight May 7. Project ABSTRACTS Click Here Sample Project ABSTRACT UPDATES March Update samples Click Here
Tue Mar 5	Lab 4: Equilibrium Temperature Distributions (Ref: §2.5 Exercise 31). Meet in computer lab LCB 115, 1:45pm. Due by Mar 29. Lab session resources Here
Mar 9-17	Week 10: Spring Break, no classes
Mar 18-22	Week 11: Appendix B: Review of complex numbers, §5.2 The characteristic equation, §5.3 Diagonalization, §5.4 Eigenvectors and linear transformations. Chapter 5 Slides: Here, Friday HW: Here Project ABSTRACTS Orig abstracts Click Here Project ABSTRACT UPDATES March Updates Click Here
Tue Mar 19	Lab 5: Hill Substitution Ciphers (Ref: §4.1). Meet in computer lab LCB 115, 1:45pm. Due by May 7. A quick-start file appears in the maple/lab5 Directory (see file lab5-hillcipher-problems-1-6.mw). Kindly right-click and save the link to your Desktop. Then load it into xmaple and edit it, to get started. Lab 5 has caused lost time for many due to off-by-one errors: use the quick-start file above!
Thu Mar 21	ONE WEEK WARNING: Exam 2 is Friday March 29, 12:50pm to 1:50pm. Sample Exam 2 on Chapters 1 to 5 for S2019: Questions and Answers Old Exams 1 and 2 from S2018, covers all 3 exams in S2019: Questions and Answers 2018 Exam 1 and Questions and Answers 2018 Exam 2
Mar 25-29	Week 12: §5.5 Complex eigenvalues, §5.6 optional, Discrete Dynamical Systems, §5.7 optional, Applications to differential equations, §5.8 optional, Iterative Estimates for Eigenvalues, §6.1 Inner product, length and orthogonality, §6.2 Orthogonal sets, §6.3 Orthogonal projections, Iris dataset and PCA: Link to article Eigenpairs in maple, plots of eigenvectors: see eigenvector-plots-25mar2019.mw (also .pdf) here: Maple Examples Directory Commutative Diagrams and Matrix of a transformation (sec 5.4): Directory, see commativeDiagram.pdf Orthogonal complement and the cross-product: orthogonality.pdf Ch6 Slides and manuscripts HERE Friday HW: Here. Chapter 6 Slides: Here. Exam 2 references are in the Ch6 directory. Maple examples from class are found HERE. The sources are .mw, .mpl (text) and PDF with file name containing 28mar2018. The examples are 2x2 and 3x3 diagonalization AP=PD with A, P, D real matrices, complex eigenvalues. Exam 2 Review, JFB 102, 1:45-3:30pm Monday March 25: Blackboard photo directory EXAM 2: 12:50-1:50pm Friday March 29 Link to Student Solutions to 2019 Midterm 2 (uploaded 5 Apr 2019) Grading Table used for Exam 2 JPG HERE HW12 and maple labs are due Monday April 1. Nothing collected on 29 March (exam day).
Apr 1-5	Week 13: §6.4 The Gram–Schmidt process and QR decomposition, §6.5 Least-squares problems, intro §6.6 optional, Application to linear models, §6.7 optional, Inner product spaces, §6.8 optional, Applications of Inner Product Spaces, Fundamental Theorem of Linear Algebra: PDF Slides HERE (revised Apr 1, 2019) Independence of basis for definition of orthogonal projection Lecture Photos HERE Exercises 6.4-24, 6.5-26, 6.6-13 with maple presentations: MAPLE-EXAMPLES DIRECTORY Decomposition A=QR in advancedTopicsLinearAlgebra.pdf, located in Chapter 6 slides/manuscripts HERE, Due Monday: work from Week 12, HW12 and maple labs. Friday HW: Here is due May 7

Course Calendar Weeks 14-16

Thu Apr 11	Lab 6, Fibonacci and Lucas Sequences is due by May 7. Meet in computer lab LCB 115, 1:50pm 2018: Sean Johnson found an error in Problem 7. Error corrected in sources. Problem 7: Use the PDF and Worksheet files named lab6-fibonacci-lucas-sequences-problem7-computation in the Lab6 sources: Lab 6 Source Directory: Click Here (see files containing lcb115 for Headstart source code) Optional Lab 7, Polynomial Roots and the QR Method is due by May 7, replaces any missing Lab Lab 5 due May 7 has caused lost time for many due to off-by-one errors. Load the rewritten upstart file lab5-hillcipher-problems-1-to-6 located HERE
Apr 8-12	Week 14: §6.5 Least-squares problems, continued with Exercises 6.5-26 and 6.6-13, §7.1 Diagonalization of symmetric matrices, Friday HW: Here is due May 7. Project Presentation Details will be sent to you in email after 12 April. EXPECTED: A newly crafted abstract and a draft of your presentation, if you wish to preset. Presenters receive grade "A". Chapter 6 Slides: Here, especially files advancedTopicsLinearAlgebra.pdf, orthogonality.pdf, fundTheoremLinearAlgebra.pdf and InvertibleMatrixTheorem.pdf (all parts a to x). EXAM 3 Review: Tuesday 9 April, 12:55-1:45pm in JFB 102 (regular classroom). Sample Exam 3 PDF Sample April 9 blackboard photos of Exam3 sample solutions problems 2,3,5 have been posted: HERE Answers and solutions to sample exam 3: TEXT HERE
Apr 12	EXAM 3: 12:50-1:50pm Friday April 12 Link to Student Solutions to 2019 Midterm 3 (uploaded 16 Apr)
Apr 15-19	Week 15: §7.2 Quadratic Forms (Ellipse and Ellipsoid, conic sections), §7.3 Optional Constrained Optimization, §7.4 The singular value decomposition, §7.5 Optional Applications to Image Processing and Statistics. Friday HW: Here [last homework] due May 7. Chapter 6 Slides: Here, especially file advancedTopicsLinearAlgebra.pdf, orthogonality.pdf, fundTheoremLinearAlgebra.pdf and InvertibleMatrixTheorem.pdf (all parts a to x). Four Fundamental Subspaces and matrices U, V: PNG HERE (uploaded 19 Apr) Four Fundamental Subspaces: PNG Image Here. [Don't use it. An example of useless internet dribble.] Strang's Newspaper Article on the Four Subspaces HERE Solutions to Exam 1, Exam 2 and Exam 3 can be found below in Week 16.
Apr 22,23	Week 16: Student Presentations of Selected Projects Directories Here. Photos from the two days of presentations are in the above directory. After the presentations, Final Exam Review begins Wednesday 24 Apr at 4:30PM in LCB-215. Mon-Tue 22-23 April presentation titles and presenters: PDF SCHEDULE
Apr 24	Classes end. Office hours end. Projects due by Midnight May 7 by email. Submit no paper. Project must be PDF. Submit in addition DOC, DOCX and a ZIP file for computer code. Send to Dr G at this Email Address Solutions to S2019 Exams 1, 2 and 3 Exam 1 S2019 Typeset Solutions Exam 2 S2019 Student Solutions Exam 3 S2019 Student Solutions Final Exam Review. Location and time: LCB 215 at 4:30pm until 6:30pm on Wednesday April 24 The review used the 2018 Final Exam for discussion of problems. Link to 24 Apr Final Exam Review Photos Here (uploaded 25 April) Problem statements and student solutions found HERE (2018 Final Exam) Published Projects for Spring 2019 are found Here
Tuesday Apr 30	Final Exam 1:00 to 3:00pm in JFB-102. Link to Questions and Student Solutions to 2019 Final Exam (uploaded 7 May) 2019 Sample final exam: Questions and Answers S2019 2018 Sample final exam: Questions and Answers S2018 Old Sample final exam: Questions and Answers S2017 (duplicated in S2018) Old Sample final exam: Questions and Answers S2016 (duplicated in S2017, S2018) Sample Final Exam 2015 [Professor Lesieutre] Questions and Answers Old final exam: Questions and Student Solutions 2018 Final Exam Final Exam Questions Only 2017and Final Exam student solutions S2017 Old final exam: Final Exam Questions S2016 ( Handwritten Student Solutions) Old S2012 sample final exam: Questions and Answers from S2012 Old S2012 final exam: Questions and Answers from S2012 Cachen's final exam F2010: Here Cachen's's F2010 final exam study guide and essay question info Here.

Homework, Labs, Problem Sessions, Extra Credit, Semester Project

Homework Packages

Homework is normally started in the 7-day period before the Friday due date.
A complete list of exercises to be submitted for grading:

1.1: 7, 11, 19, 25, 34.
1.2: 1, 7, 11, 13, 15, 17, 19, 23, 25, 28, 33
1.3: 11, 13, 15, 21, 25, 34
1.4: 6, 8, 17, 23, 27, 31, 32
1.5: 7, 8, 10, 29, 31, 33, 35
1.6: 1, 7, 13
1.7: 7, 13, 17, 27, 37
1.8: 17, 20, 25, 31
1.9: 15, 25, 31, 39
2.1: 13, 18, 23, 28, 29
2.2: 11, 23, 24, 35;
2.3: 7, 13, 14, 17, 19, 20, 21, 33, 35
2.4: 3, 5, 15, 21, 23
2.5: 3, 7, 11, 25
3.1: 5, 9, 11, 15, 25, 27, 29, 31
3.2: 5, 9, 15, 19, 25
3.3: 3, 5, 13, 19, 31
4.1: 1, 5, 7, 11, 13, 21, 27
4.2: 3, 5, 11, 15, 23, 31
4.3: 5, 9, 11, 13, 15, 19, 34
4.4: 3, 7, 9, 13, 27
4.5: 5, 7, 11, 13, 21
4.6: 1, 3, 5, 7, 15, 21
5.1: 7, 13, 17, 23, 29, 37(M)
5.2: 3, 7, 13, 17, 25(M)
5.3: 5, 9, 19, 29, 35(M)
5.4: 5, 9, 11, 15
5.5: 5, 9, 13, 19
6.1: 11, 13, 17, 29, 31
6.2: 9, 11, 13, 15, 21, 27
6.3: 1, 3, 9, 11, 15
6.4: 5, 11, 13, 19
6.5: 3, 5, 7, 11, 15, 25
7.1: 9, 13, 17, 19, 35
7.2: 5, 7, 11, 17(M)
7.3: 1, 5, 9
7.4: 3, 7, 13, 15, 17, 23

Printable file of the list above, with week due: Bookmark TEXT File Here.

Week 1 [start Monday Jan 7, due Friday Jan 11]

Week 2 [start Jan 11, due Jan 18] Week 3 [start Jan 18, due Jan 25]

Week 4 [start Jan 25, due Feb 1] Week 5 [start Feb 1, due Feb 8]

Week 6 [start Feb 8, due Feb 15] Week 7 [start Feb 15, due Feb 22]

Week 8 [start Feb 22, due Mar 1] Week 9 [start Mar 1, due Mar 8]

Week 10 [Spring Break Mar 9 to 17, nothing due]

Week 11 [start Mar 8, due Mar 22]

Week 12 [start Mar 22, due Mar 29] Week 13 [start Mar 29, due by May 7]

Week 14 [start Apr 5, due by May 7] Week 15 [start Apr 12, due by May 7]

Maple Labs

Maple labs 1 to 6 are due as indicated, usually 7 days or more after the LCB 115 session. The labs are distributed in PDF format and also in MW and MPL formats suited for input into Maple. Download what you need from the Maple Labs Directory

Utah Maple Help gives examples of maple coding that can be mouse-copied into a maple session. Recorded here is how to setup maple as a worksheet, how to print and how to save files. Also find here how to use the laylinag package described in the 2270 textbook (Lay, Lay, Calvis 2015). Questions arising from these documents can be answered in the Math Center, by email to me, in person 113 JWB or phone (801-581-6879).
Click Here for Utah Maple Help 2019

Lab 1: Due at the last February class (by Mar 1)

Lab 2: Traffic Flow Due at the last February class (by Mar 1).
Resources and corrections are located in the Lab 2 source Directory

Lab 3: Adjacency Matrices and Airline Routes Due at the last March class

Lab 4: Equilibrium Temperature Distributions Due at the last March class

Lab 5: Hill Substitution Ciphers Due by May 7

Lab 6: Fibonacci and Lucas Sequences Due by May 7

Optional Lab 7: Polynomial Roots and the QR Method Due by May 7, replaces any missing Lab

Remote Maple: Running Maple from Home

Maple can be run from home, a laptop, or even a phone or tablet, using a minimal internet connection. Instructions here for the UofU Library and the Math Department computers:
Maple from home, UofU Library Remote Maple 2017 How To Use Remote Maple

Problem Sessions

The problem sessions can be scheduled for fixed times during the week. You may add or remove your name from the problem session list of days and times, by sending email. The list is updated whenever this happens.
View the Problem Session List for locations and times.
The default location is JWB 113. We would move from this office to a Math Center room, or a classroom, provided there are 3 or more persons. Problem sessions reduce to a consultation or a tutorial when there are one or two persons. We work from clipboards and computers discussing problems, textbook topics and exam questions.

Extra Credit Problems

One collection of extra credit problems are matched to Otto Bretscher's textbook on linear algebra. A second collection of extra credit problems is matched to Gilbert Strang's linear algebra textbook. Some problems are independent of any textbook. Credit is one-to-one for missed homework, whatever the reason, without any effort to match subjects or chapters from the current textbook.
Extra credit is organized by chapter: Download Extra Credit Problems Here.

Semester Project

The due date for the semester project is actually three dates.

Create or join a group by Friday, February 1. Group leaders report by email (1) the topic, (2) a summary of what will be done, and (3) a list of group members with email addresses.
The group leader submits a draft summary of the project results on March 8.
Presentation selection is the week of April 14. Submit final drafts by Midnight April 17.
The best projects will be identified and scheduled for classroom presentation on April 22 and 23.
The revised final semester project report in PDF form is due in email by Midnight May 7. A paper print of the PDF is not expected, although classroom copies and/or an internet link is recommended, if your group has a presentation on April 22 or 23.

Some topics and sample projects can be found on the Projects Page.

Published Projects for Spring 2019 are found Here

Text file of projects in progress s2019, subject to change or join/split group. Please write email (not CANVAS) to Dr G for changes. Project List Here.

Presented and submitted projects from the 2270 course in Spring 2018 appear Here.

Presented and submitted projects from the 2270 course in Spring 2017 appear Here.

Presented and submitted projects from the 2270 course in Spring 2016 appear Here.

Presented and submitted projects from the 2270 course in Spring 2012 appear Here.