Math 22704  Linear Algebra, Spring 2019 
Instructor  G.B. Gustafson, PDF Syllabus Here, HTML Syllabus Here 
Office hours  JWB 113 after class, and by appointment. (801) 5816879 Email preferred. Office Hours: Door Card Hours and Email Address. 
Lecture 
Linear Algebra 22704 meets at 12:55pm MTWF in JFB102.
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 16
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 
Jan 711 
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

Jan 1418 
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 2125 
Week 3:
§1.6 Applications of Linear System, 
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 1518, Sarrus' Rule),
§2.2 The Inverse of a Matrix.
§2.3 Characterizations of Invertible Matrices.
Friday HW:
Here.
Chapter 2 slides Here 
Tue Jan 29 
Lab
1: Intro to Maple, Meet in computer lab LCB 115, 1:45pm. Due by Mar 1.

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 48 
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 LUdecomposition Chemical Balance example from 1.6 PDF: maple shortcuts LUDecomposition 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. Exam 1 Review, 4:306pm 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 1115 
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. 
Course Calendar Weeks 713
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. 
Feb 1822 
Week 7:
No class Monday: President's Day holiday 
Feb 2528, Mar 1 
Week 8:
§4.4 Coordinate Systems,
§4.5 The dimension of a vector space,
§4.6 Rank.
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. 
Mar 48 
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: PerronFrobenius 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 917 
Week 10: Spring Break, no classes 
Mar 1822 
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

Tue Mar 19 
Lab
5: Hill Substitution Ciphers (Ref: §4.1). Meet in computer lab
LCB 115, 1:45pm. Due by May 7. A quickstart file appears in the
maple/lab5 Directory (see file lab5hillcipherproblems16.mw). Kindly rightclick and save the link to your Desktop.
Then load it into xmaple and edit it, to get started. 
Thu Mar 21 
ONE WEEK WARNING: Exam 2 is Friday March 29, 12:50pm to 1:50pm. 
Mar 2529 
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,
EXAM 2: 12:501:50pm Friday March 29

Apr 15 
Week 13:
§6.4 The Gram–Schmidt process and QR decomposition,
§6.5 Leastsquares 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 6.424, 6.526, 6.613 with maple presentations: MAPLEEXAMPLES 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 1416
Thu Apr 11 
Lab
6, Fibonacci and Lucas Sequences is due by May 7. Meet in computer lab LCB 115, 1:50pm Lab 5 due May 7 has caused lost time for many due to offbyone errors. Load the rewritten upstart file lab5hillcipherproblems1to6 located HERE 
Apr 812 
Week 14:
§6.5 Leastsquares problems, continued with Exercises 6.526 and 6.613,
§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, 12:551:45pm 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: 12:501:50pm Friday April 12 Link to Student Solutions to 2019 Midterm 3 (uploaded 16 Apr) 
Apr 1519 
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 
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 JFB102. 
Homework, Labs, Problem Sessions, Extra Credit, Semester Project
Homework Packages
Homework is normally started in the 7day 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, 23Printable 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 DirectoryUtah Maple Help gives examples of maple coding that can be mousecopied 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 (8015816879).
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 onetoone 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.