Math 22702  Linear Algebra, Spring 2018 
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 22702 meets at 8:00am MWF in JFBB1.
Computer Lab in LCB 115 on select Tuesdays. Information about Problem sessions Here. 
Midterm Exams  Exams held from 7:30am to 9:25am on Friday 23 Feb and Friday 6 Apr. 
Final Exam  Exam 7:30am to 10:00am on Monday 30 April, regular classroom. 
Textbook  David C. Lay, Linear Algebra and Its Applications, 5E (2015). Book Cover Here 
Online Grades  Web site for Utah Canvas 
Last change: Friday May 11: 18:31PM, 2018 
Course Calendar Weeks 16
First Week 
First exercise package
Here is due on Friday of Week 1 [12 Jan]. If the bookstore has no 2270 textbooks, then get the first chapter here: Chapter 1 The Math Center 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 812 
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

Monday Jan 15 
Martin Luther King Day, no university classes 
Jan 1619 
Week 2:http://www.math.utah.edu/~gustafso/s2017/2270/projects2017/projectList2017RevisedMarch26noEmail.txt
Monday no class. 
Jan 2226 
Week 3: §1.6 Applications of Linear System, §1.7 Linear Independence, §1.8 Introduction to Linear Transformations. Friday HW: Here 
Jan 29 to Feb 2 
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 
Jan 30 
Lab
1: Intro to Maple, Meet in computer lab LCB 115, 7:30am. Due by Feb 28.

Feb 2 
Semester Project Deadline Feb 2: Create or join a project group by email. Please write email to Dr G for changes. Presentations of projects on April 20 and 23. Submit your project by email, deadline midnight May 7. 
Feb 6 
Lab 2: Traffic Flow. Meet in computer lab LCB 115, 7:30am. Due by Feb 27. 
Feb 59 
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 9 Feb TEXT: maple text and PDF: Output from the computation Chapter 2 slides Here (Determinants, PIVOT Theorem, Fund Thm Toolkit Sequences) Friday HW: Here 
Feb 1216 
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.
Exam 1 in one week. Maple from home, UofU Library Remote Maple 2017 How To Use It Project ABSTRACTS Click Here 
Course Calendar Weeks 713
Monday Feb 19 
President's Day, no university classes 
Tuesday 
Exam Review, LCB 215 4:005:30pm Review session blackboard photos directory Here 
Feb 1923 
Week 7:
No class on Monday. Exam 1 on 23 Feb. 
Feb 27 
Lab 3: Adjacency Matrices and Airline routes. Meet in
computer lab LCB 115, 7:30am. Due by Mar 31. Maple from home, UofU Library Remote Maple 18 How To Use It 
Feb 2628, Mar 12 
Week 8:
§4.4 Coordinate Systems,
§4.5 The dimension of a vector space,
§4.6 Rank.

Mar 59 
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. Chapter 5 Slides: Here, Friday HW: Here Project Deadline: Group leader submits project draft by Mar 9. Final copy due by Midnight May 7. Project ABSTRACTS Click Here 
Mar 6 
Lab 4: Equilibrium Temperature Distributions (Ref: §2.5 Exercise 31). Meet in computer lab LCB 115, 7:30am. Due by Mar 31. Lab session resources Here 
Mar 1216 
Week 10:
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 Click here for Solutions to 2018 Midterm 1(uploaded 11 Mar) Project ABSTRACTS Orig abstracts Click Here Project ABSTRACT UPDATES March Updates Click Here 
Mar 13 
Lab 5: Hill Substitution Ciphers (Ref: §4.1). Meet in computer lab LCB 115, 7:30am. Due by May 7. A transcript of the session appears in the Labs Directory (see file lab5hillcipherproblems12.mw) Lab 5 has caused lost time for many due to offbyone errors. Load the rewritten upstart file lab5hillcipherproblems125 located HERE 
Mar 1725 
Week 11: Spring Break, no classes 
Mar 2630 
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,
Friday
HW:
Here.
Chapter 6 Slides:
Here. Exam 2 references are in the Ch6 directory. ONE WEEK WARNING: Exam 2 is Friday April 6, 7:30am to 9:30am. Study all the resources linked in
Week 13 (April 6). Especially, study the sample exam and Exam 2 from 2017: 
Apr 26 
Week 13: §6.3 Orthogonal projections, §6.4 The Gram–Schmidt process. Friday HW: Here is due May 7 
Exam 2 Review, 4:306pm April 3  Blackboard photo directory (uploaded 3 April 2018) 
Apr 6 
Exam 2. 
Course Calendar Weeks 1416
Apr 10 
Lab
6, Fibonacci and Lucas Sequences is due by May 7. Meet in computer lab LCB 115, 7:30am Lab 5 has caused lost time for many due to offbyone errors. Load the rewritten upstart file lab5hillcipherproblems125 located HERE 
Apr 913 
Week 14:
§6.4 The Gram–Schmidt process (continued); reference for A=QR in advancedTopicsLinearAlgebra.pdf,
§6.5 Leastsquares problems,
§6.6 optional, Application to linear models,
§6.7 optional, Inner product spaces,
§6.8 optional, Applications of Inner Product Spaces,
§7.1 Diagonalization of symmetric matrices,
Friday HW:
Here is due May 7. Project Presentation Details to be sent in email on 13 April. Chapter 6 Slides: Here, especially files advancedTopicsLinearAlgebra.pdf and InvertibleMatrixTheorem.pdf (all parts a to x). Midterm 2 returned 18 Apr. Link to Solutions to Midterm 2 (uploaded 23 April) 
Apr 1620 
Week 15:
§7.2 Quadratic Forms,
§7.3 Constrained Optimization,
§7.4 The singular value decomposition,
§7.5 Optional Applications to Image Processing and Statistics. Friday Apr 20: Student Presentations of Selected Projects Directories Here Friday HW: Here [last homework] due May 7. Chapter 6 Slides: Here. Solutions to Exam 1 and Exam 2 can be found below in Week 16. 
Apr 23 
Week 16: Student Presentations of Selected Projects (continued) 
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 S2018 Exams 1 and 2 Exam 1 S2018 Typeset Solutions Exam 2 S2018 Student Solutions Final Exam Review. Location and time: LCB 215 at 4:30pm until 6:30pm on Tuesday April 24 Link to Final Exam Review Photos Here (uploaded 25 Apr) Published Projects for Spring 2018 are found Here [uploaded May 11, 2018]. 
Monday Apr 30 
Final Exam 7:3010:00 am in JFBB1. 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 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 8, due Friday Jan 12]
Week 2 [start Jan 12, due Jan 19] Week 3 [start Jan 19, due Jan 26]
Week 4 [start Jan 26, due Feb 2] Week 5 [start Feb 2, due Feb 9]
Week 6 [start Feb 9, due Feb 16] Week 7 [start Feb 16, due Feb 23]
Week 8 [start Feb 23, due Mar 2] Week 9 [start Mar 2, due Mar 9]
Week 10 [start Mar 9, due Mar 16]
Week 11 [Spring Break Mar 17 to 25, nothing due]
Week 12 [start Mar 16, due Mar 30] Week 13 [start Mar 30, due Apr 6]
Week 14 [start Apr 6, due Apr 13] Week 15 [start Apr 13, due 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 2018
Lab 1: Due at the last February class
Lab
2: Traffic Flow Due at the last February class.
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 18 How To Use Remote Maple
Problem Sessions
The problem sessions are 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 consultations or tutorials 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 2. 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 9.
 The best projects will be identified and scheduled for classroom presentation
on April 20 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 20 or 23.
Some topics and sample projects can be found on the Projects Page.
Published Projects for Spring 2018 are found Here [uploaded May 11, 2018].
Text file of projects in progress s2018, 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 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.