Course Calendar Weeks 16
First Week 
First exercise package
Here is due on Friday of Week 1 [15 Jan]. The bookstore has no 2270 textbooks. Get the first chapter here: Chapter 1 The Math Center is open, with study areas, computers and free tutoring: Read this memo for details. 
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. 
Jan 1115 
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 18 
Martin Luther King Day, no university classes 
Jan 1922 
Week 2: Monday no class, §1.4 The Matrix Equation A x = b , §1.5 Solution Sets of Linear Systems. Friday HW: Here. Chapter 1 slides Here 
Jan 2529 
Week 3: §1.6 Applications of Linear System, §1.7 Linear Independence, §1.8 Introduction to Linear Transformations. Friday HW: Here 
Feb 15 
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 
Feb 2 
Lab
1: Intro to Maple, Meet in computer lab LCB 115, 7:30am. Due by Fri, Feb 26.

Feb 9 
Lab 2: Traffic Flow. Meet in computer lab LCB 115, 7:30am (was Feb 16). Due by Mon, Feb 29. 
Feb 812 
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.
Project Deadline: Create or join a group. YouTube video on LUdecomposition Friday HW: Here 
Feb 15 
President's Day, no university classes 
Feb 1519 
Week 6: Monday no class, §3.2 Properties of determinants, continued, §3.3 Cramer’s rule, volume and linear transformations. Exam 1. Friday HW: Here. Chapter 3 slides Here Maple from home, UofU Library Remote Maple 18 How To Use It 
Feb 19 
Exam 1. 
Course Calendar Weeks 713
Feb 2226 
Week 7:
Summary of delayed section §2.8 Subspaces of R^n,
§4.1 Vector spaces and subspaces,
§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. 
Mar 1 
Lab 3: Adjacency Matrices and Airline routes. Meet in
computer lab LCB 115, 7:30am Maple from home, UofU Library Remote Maple 18 How To Use It 
Feb 29 to Mar 4 
Week 8:
§4.4 Coordinate Systems,
§4.5 The dimension of a vector space,
§4.6 Rank.

Mar 711 
Week 9:
§4.7 Change of basis,
§4.8 optional, Applications to Difference Equations,
§4.9 optional, Applications to Markov chains,
§5.1 Eigenvectors and eigenvalues,
Appendix B: Review of complex numbers. Chapter 5 Slides: Here, Friday HW: Here 
Mar 14 to 18 
Week 10: Spring Break, no classes 
Mar 22 
Lab 4: Equilibrium Temperature Distributions (Ref: §2.5 Exercise 31). Meet in computer lab LCB 115, 7:30am. Lab session resources Here 
Mar 2125 
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 
Mar 29 
Lab 5: Hill Substitution Ciphers (Ref: §4.1). Meet in computer lab LCB 115, 7:30am. A transcript of the session appears in the Labs Directory (see file lab5hillcipherproblems12.mw) 
Mar 28 to Apr 1 
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, Project Deadline: Group leader submits project draft. Final copy due May 2. Friday HW: Here. Chapter 6 Slides: Here. 
Apr 48 
Week 13: §6.3 Orthogonal projections, §6.4 The Gram–Schmidt process. Friday HW: Here is due May 4 
Apr 8 
Exam 2. 
Course Calendar Weeks 1416
Week 14: Apr 1115 
Apr 12: Lab2270finalsolutionsstudentS2016
6, Fibonacci and Lucas Sequences is due May 2. Meet in computer lab LCB 115, 7:30am 
Apr 1115 
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,2270finalsolutionsstudentS2016
§7.2 Quadratic Forms.
Friday HW:
Here is due May 4. Semester Project email 13 April Project Presentation Details, 
Apr 1822 
Week 15:
§7.3 Constrained Optimization,
§7.4 The singular value decomposition,
§7.5 Optional Applications to Image Processing and Statistics. Apr 22: Student Presentations of Selected Projects Semester Project topics: Project Presentation Updated List, Friday HW: Here [last homework] due May 4. 
Apr 25 
Week 16: Student Presentations of Selected Projects (continued) and Final Exam Review. 
Apr 26 
Classes end. Office hours end. Projects due on Monday May 2 Published Projects for Spring 2016 can be found Here. 
Thursday Apr 28 
Final Exam 7:3010:00 am in AEB 320. Gustafson's final exam S2012: Questions and Answers Cachen's final exam F2010: Here Cachen's's F2010 final exam study guide and essay question info Here. 
Syllabus
Math 22702 Linear Algebra
Instructor.
Professor Grant B. Gustafson
Email: See the online door card: Here.
Office: JWB 113
Syllabus: HTML
Here.
Course Web page, access to all files: Directory Here
Office Hours: MWF after class in JWB 113
Additional office hours Here.
Meetings.
Time: MWF 8:00am until 9:20am
Location: AEB 320
Prerequisites. MATH 2210 OR MATH 1260 OR MATH 1280
Textbook. Linear Algebra and Its Applications, Fifth Edition by David C. Lay et al, ISBN 9780321982384 and
ISBN 032198238X.
Supplement:
Student Study Guide for Linear Algebra and Its Applications 5th Edition, David C. Lay el (2015).
ISBN13: 9780321982575 and
ISBN10: 0321982576.
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 bookmark file of the list above, with week due, Here.
Week 1 [start Monday Jan 11, due Friday Jan 15]
Week 2 [start Jan 15, due Jan 22] Week 3 [start Jan 2, due Jan 29]
Week 4 [start Jan 29, due Feb 5] Week 5 [start Feb 5, due Feb 12]
Week 6 [start Feb 12, due Feb 19] Week 7 [start Feb 19, due Feb 26]
Week 8 [start Feb 26, due Mar 4] Week 9 [start Mar 4, due Mar 11]
Week 10 [Spring Break Mar 12 to 20, nothing due]
Week 11 [start Mar 11, due Mar 25] Week 12 [start Mar 25, due Apr 1]
Week 13 [start Apr 1, due Apr 8] Week 14 [start Apr 8, due Apr 15]
Week 15 [start Apr 15, due Apr 22]
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 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, or in person 113 JWB or phone (8015816879).
Utah Maple Help 2016
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 May 2
Lab 6: Fibonacci and Lucas Sequences Due May 2
Optional Lab 7: Polynomial Roots and the QR Method Due May 2, 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 It
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 classroom or Math Center room, provided there are 3 or more persons. Problem sessions reduce to tutorials when there are one or two persons. We work from clipboards and computers, discussing problems 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.
The extra credit PDF files, organized by chapter, are located Here.
Semester Project
The due date for the semester project is actually three dates. Create or join a group by Friday, February 12. Group leaders report by email (1) the topic, (2) a summary of what will be done, and (3) a list of group members.
 The group leader submits a draft summary of the project results on April 1.
 The best projects will be identified and scheduled for classroom presentation
on April 22 and 25.
 The revised final semester project report in PDF form is due in email by May 2. 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 25.
Some topics and sample projects can be found on the Projects Page Here.
Published Projects Spring 2016. Presented projects and all submitted projects appear Here.
Presented and submitted projects from the 2270 course in Spring 2012 appear Here.