Linear Algebra and its Applications 5th edition by Lay et al, Pearson; ISBN-13:  978-0-321-98238-4

MTH 215 Linear Algebra

Spring 2020 - Course Webpage
James Baglama
Office: Lippitt Hall 200
Department of Mathematics

Linear Algebra and its Applications 5th edition by Lay et al, Pearson; ISBN-13:  978-0-321-98238-4


Final Exam will be available in Sakai under Tests and Quizzes tool from 12:00am Monday May 4 to 11:55pm Friday May 8. Time limit will be 5 hours. The Final Exam is 50 multiple choice questions and you have two attempts on the final exam. The best score will be recorded.




Octave online

MTH 215 Spring 2020 Course Calendar and Slides

MTH 215 Syllabus

Sakai is being used in part for this course. The Sakai site will contain your grades and any details on class activities (e.g. projects) You can access Sakai at the following web address: Use your e-campus id and your URI Webmail password.

Academic Enhancement Center (AEC) and Math Department Tutoring

Illness Due to Flu
If you develop flu-like symptoms, please stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class or to my office. Please notify me via email of your status. We will work together to ensure that the course work is completed for the semester.


Software for the course

Example using Row ops in Matlab/Octave

A = [1 2 3; 0 1 0; 1 1 1]

and Matlab/Octave responds with

A =

1 2 3

0 1 0

1 1 1

You enter row by row, separating rows with semicolons. Between row elements, you can use spaces or commas.

Matlab/Octave elementary row operations.

Ex. R1 <---> R3

A([1 3],:) = A([3 1],:)

Ex. 2*R3 ---> R3

A(3,:) = 2*A(3,:)

Ex. 5*R2 + R1 ---> R1

A(1,:) = A(1,:) + 5*A(2,:)





Course and Section number: MTH 215 Section 01
Course Title: Linear Algebra
Semester and Year: Spring 2020
Class Day(s)/Time:: MWF, 12:00pm to 12:50pm
Class Location: Lippitt Hall 204
Instructor: James Baglama
Office Location: Lippitt Hall 200
Office Hours: MW 11:00am to 11:50am
Contact Information Phone:401.874.2709 and Email:j(mylastname)(AT)

Course Description: LEC: (3 crs.) Detailed study of finite dimensional vector spaces, linear transformations, matrices, determinants and systems of linear equations.

Prerequisite(s): C- or better in MTH 131, 141, 180, or equivalent.

General Education Area(s) and Outcome(s): None

Credit Hours: 3

Required Textbook(s): Linear Algebra and its Applications 5th edition by Lay et al, Pearson; ISBN-13: 978-0-321-98238-4

Other Required Material(s): You may use a calculator for homework and exams to do routine calculations. You will need to use Octave or Matlab for the project(s). Octave online:

Course Goals: Linear algebra is a branch of mathematics that studies systems of linear equations, vector spaces, linear transformations, and the properties of matrices. Students will be able to apply the concepts and methods of linear algebra that play an essential role in mathematics and in many technical areas of modern society, such as computer science, data science, engineering, physics, environmental science, economics, statistics, business management, and social sciences.

Learning Outcomes: At the end of the course the student will be able to:

  1. solve a linear system of equations by using row operations;
  2. represent linear systems in different formats;
  3. compute basis vectors and detemine linear independence of vectors;
  4. write general solutions to linear systems;
  5. perform matrix and vector operations (e.g. addition, subtraction, multiplication, and scalar multiplication);
  6. compute the inverse of matrix;
  7. compute rank and null space of a matrix;
  8. work with linear transformations;
  9. work within vector spaces and subpsaces;
  10. compute determinants;
  11. compute eigenvalues and eigenvectors;
  12. use technology to analyze methods and perform calculations;
  13. communicate effectively in written form mathematical ideas and conclusions, by stating in a complete, clear, concise, and organized manner steps, calculations, solution strategy, conclusions, and when appropriate, interpreting results in practical or applied terms.

Grade Distribution:
15% Projects See Projects below
15% Homework See updated remote instruction below
40% Exams Three TWO exams (2/21, See updated remote instruction below )
30% Final Exam See updated remote instruction below

Letter Grade Distribution:
92 - 100 A 72 - 76 C
90 - 91 A- 70 - 71 C-
87 - 89 B+ 67 - 69 D+
82 - 86 B 60 - 66 D
80 - 81 B- 0 - 59 F
77 - 79 C+

Instructor Policies for the Course:

  • Assignments
    See updated remote instruction below
    Homework will be assigned for section of the textbook we cover. A list of homework problems is posted on this website. Do NOT email your homework to me! Homework must have
    • your name
    • chapter and section number
    • list of problems assigned
    • complete solution (answers only will be given no credit)
    • multiple pages stapled or corners folded with pages numbered and your name on each page.
    If I cannot read it or follow the solution, then it is marked incorrect. Pencils only please. I will not accept ANY late or incomplete homework assignments.
  • Attendance
    See updated remote instruction below
    Attendance is a vital and necessary part of this course. While there is no formal attendance policy, we cover a lot of information at a rapid pace; missing a class will result in a large amount of material missed. Students are responsible for all missed work, regardless of the reason for absence. It is also the absentee's responsibility to get all missing notes or materials.
  • Expectations
    See updated remote instruction below
    • You are expected to attend every lecture, and to submit your work on time. Late homework is not accepted.
    • It is your responsibility to clearly communicate your solutions for homework, projects, and exams. Your results (answers) must display a strong understanding of the material and be written in a correct, complete, coherent, and well-organized fashion.
    • The rapid pace of the class requires that you spend time every day doing homework, reviewing notes, reading the textbook, and working out extra problems.
  • Makeup Policy
    See updated remote instruction below
    Makeup exams may be scheduled in the event you are unable to attend exams under the following conditions. See University Manual sections 8.51.10 to 8.51.14 for guidelines.
    • If the reason for missing the exam as scheduled is (i) a University sanctioned event for which verifiable documentation can be provided, (ii) a responsibility to an employer or scheduled job interview that cannot be rescheduled, or (iii) Religious holidays, then you must inform your instructor 48 hours in advance of the exam and provide documentation if requested. Makeup exams will be scheduled after the actual exam, and preferably before the class period when exams are to be handed back, but no later than one week after the original date.
    • If the reason for missing the exam as scheduled is due to (i) illness (with verifiable documentation from a medical provider if requested), or (ii) an emergency (with appropriate documentation if requested), then you must contact your instructor (via email or phone) within 24 hours of the exam. If the illness or emergency prevents contact within 24 hours (with appropriate documentation if requested), then contact is require as soon as possible. Prolonged absence (missing 2 or more classes) will require documentation for make-up work. Makeup exams may be scheduled no later than a week after the original date, unless the illness or emergency precludes this, in which case we will follow the University Manual sections 8.51.10 to 8.51.14.
    • Missing an exam for reasons not listed above and failure to notify your instructor within 7 calendar days of your absence will result in a 0 for the exam, see section 8.51.14 Univeristy Manual.
    • Students that miss course work (not exams) under the same the conditions mentioned above (e.g. illness) will be given an opportunity to make up the course work. Due dates will be discussed and determined on an individual basis.
    • All course work excepting the final examination must be completed by the final class meeting. See University Manual section 8.51.17
  • Electronic Devices
    Cell phones, ipads, ipods, etc. should be turned off during class. Excepted from this are electronic devices used for notetaking.
  • Other Policies
    • All class materials (e.g. notes, projects, exams, lectures, etc.) are property of URI and the instructor. Copying, video taping, taking pictures, or posting this material is not allowed without consent of the instructor. See University Manual section 8.27.22 .
    • Please come to class prepared by reading over the section of text that will be covered and by bringing your book, notebook and pencil.
    • You are here to learn, so please give class your full attention, ask questions if you do not understand and be respectful and courteous to your fellow students and professor.

Academic Honesty Policy: Cheating is defined in the University Manual as the claiming of credit for work not done independently without giving credit for aid received, or any unauthorized communication during examinations. Students are expected to be honest in all academic work. The resolution of any charge of cheating or plagiarism will follow the guideline set forth in the University Manual 8.27.10-8.27.21,

Accommodations for Special Needs: Students with Disabilities: Your access in this course is important. Please send me your Disability Services for Students (DSS) accommodation letter early in the semester so that we have adequate time to discuss and arrange your approved academic accommodations. If you have not yet established services through DSS, please contact them to engage in a confidential conversation about the process for requesting reasonable accommodations in the classroom. DSS is located in room 302 of the Memorial Union, 401-874-2098, email:

Incomplete Grade: University of Rhode Island regulations concerning incomplete grades will be followed. See University Manual sections 8.53.20 and 8.53.21 for details.

Religious holidays: It is the policy of the University of Rhode Island to accord students, on an individual basis, the opportunity to observe their traditional religious holidays. Students desiring to observe a holiday of special importance must provide written notification to your instructor.

Standards of behavior: Students are responsible for being familiar with and adhering to the published Community Standards of Behavior: University Policies and Regulations" which can be accessed in the University Student Handbook ( If you must come in late, please do not disrupt the class. Please turn off all cell phones or any electronic devices.


Projects The goals of a project are to use the concepts from linear algebra to solve real life applications. You can work in groups, no more than 4 students per group. You must use a computer software system to solve these applications. Octave is very easy to use and is free. You can also use Matlab. You can NOT use a graphing calculator or code written by someone who is not in your group. All projects must be submitted through Sakai using the Assignment tool and ALL members of the group must upload the project. Do NOT email the projects to me! Projects must have a list of all the names of students in your group. I will not accept ANY late or incomplete projects.
    ProjectDue Date
1 Project 1 (GPS Linear Systems)
11:55pm Fri. Feb. 14
2 Project 2 (Graphs)
11:55pm Fri. Mar. 27 (new date)
2 Project 3 (Error detect/correct)
11:55pm Fri. Apr. 24


Calendar and Slides

See updated remote instruction below for updated calendar

The following calendar gives a timetable for the course. We might be slightly behind or ahead at any given time. Check here often, as the Calendar will be updated according to the pace of the class. Note: In the problem lists, a notation like 3-9 means that all the problems 3,4,5,6,7,8,9 are assigned.
         Week   Events Resources/Practice Section/Notes Homework Problems Due Date     
1 Jan. 20 - Jan. 24             First Day
Wed. Jan. 22
2x2 Linear system graph
Example 1
Example 2
Example 2-Ans
Example 2a
Section 1.1
(Section 1.1) 1, 2, 7, 8, 11, 13, 19-22, 25, 30, 31, 32
(1.1) 1/29
2 Jan. 27 - Jan. 31   Example 3
Example 4
Example 4 Answers
Adding vectors
Linear combinations(1)
Linear combinations(2)
Section 1.2
Section 1.3
(Section 1.2) 1, 3, 7-12 15, 17,20, 23, 28
(Section 1.3) 1, 3, 5, 11, 13, 17, 19, 25
(1.2) 2/3
(1.3) 2/5
3 Feb. 3 - Feb. 7   Project 1

Example 5
Example 5 Answers
Example 6
Example 6 Answers
Practice in Span
Plan in R3
Section 1.4
Section 1.5
(Section 1.4) 1, 3, 5, 9, 12, 13, 15, 17, 21, 25, 32
(Section 1.5) 3, 5, 9, 11, 13, 17, 19, 21, 29-33
(1.4) 2/10
(1.5) 2/12
4 Feb. 10 - Feb. 14 Project 1
Fri. Feb. 14
Linear Independent?
Graph Transformation
Exam 1 Review(1 of 2)
Exam 1 Review(2 of 2)
Exam 1 Review Answers(1 of 2)
Exam 1 Review Answers (2 of 2)
Section 1.7
Section 1.8
(Section 1.7) 3, 5, 7, 9, 13, 15, 16, 19, 26, 27, 33
(Section 1.8) 1, 3, 7, 9, 11, 13, 17, 19, 27, 31, 32
(1.7) 2/17
(1.8) 2/19
5 Feb. 17 - Feb. 21 Exam 1 (Chapter 1)
Fri. Feb. 21
Matrix Transformation Section 1.9
(Section 1.9) 1, 2, 5, 7, 9, 17, 19
(1.9) 2/24
6 Feb. 24 - Feb. 28   Abe.txt
Large Matrices
Project 2

Erdős Number
Matrix Prod (row)
Practice Matrix-Products
Practice Matrix-Products Answers
Section 2.1
Section 6.1 (Angle)
(Section 2.1) 1, 3, 5, 7, 9, 13, 17, 23, 24, 27
(Section 6.1) 1, 5, 7, 10, 13, 23
(compute angle between u and v for 23)
(2.1) 3/2
(6.1) 3/6
7 Mar. 2 - Mar. 6   Compute Matrix Inverse
Practice Inverse
Practice Inverse Answer
Section 2.2
Section 2.3
(Section 2.2) 1, 3, 5, 7, 8, 12, 13, 17, 18, 24, 31, 33
(Section 2.3) 1, 3, 7, 8, 9, 13, 15-17, 22
See update below
Spring Break     March 9 - March 13     Spring Break




The Sakai site for the course is set up with different chat rooms for questions on Sections (including homework), WeBwork, and Projects. I will be in the chat rooms MWF 12pm to 1pm. Questions posted outside those times will be answered, but not as quickly.


The Sakai email system Messages will be used for all emails for this course. Please use this system for all future communcations vi email. When sending an email through this system to me, please check the box, Send a copy of this message to recipients' email address(es).


Sakai Tests and Quizzes Tool will be used for Exam 2 and the Final Exam.

  • Exam 2 will be available 12:00am Wednesday April 1 to 11:55pm Friday April 3. Time limit will be 2 hours. Exam 2 will be 25 multiple choice questions and you will have two attempts on the exam. The best score will be recorded.
  • Exam 3 Canceled.
  • Final Exam will be available 12:00am Monday May 4 to 11:55pm Friday May 8. Time limit will be 5 hours. The Final Exam will be 50 multiple choice questions and you will have two attempts on the final exam. The best score will be recorded.


I will create short video lectures. The links will be posted in the calendar below and in the Sakai course website. The video lectures will start with Chapter 3. Please do let me know if there are errors or omissions in any of the videos. When finding an error, please send me the time mark when it occurred in the video. Videos for Chapter 3 have been created and links are provided below.


Textbook Problems (NOT GRADED)
The textbook practice problems will not be collected/graded for the rest of the semester. The problems are listed for you to practice, ask questions in the Sakai Chat Room (during remote instruction), and help prepare you for the GRADED WeBWork online homework sets and course exams. I cannot accept any written homework prior to section 2.2 that was assigned with a due date before Spring break.

WebWork Homework (GRADED)
For the rest of the semester we will use online homework. Online homework will be administered using the free system WeBWorK.


Your username is your URI 9-digit student ID number and your default password is the first eight letters of your last name in all lowercase letters. Ignore spaces and characters other than letters. Use your entire last name if it contains eight or less letters.

Some examples:
Tim Smith, Jr., password: smithjr
Bob Jones-Smith, password: jonessmi
John O'Sullivan, password: osulliva

Please change your password as soon as you log in.

WeBWork assignments will start on Monday March 23 with sections 2.2 and 2.3.

Due dates are posted in the calendar below. All assignments are due by 11:55pm on the posted due date. There is no late or partial credit for homework. Each problem will allow 2 attempts. All problems are equally weighted (1 point).

Grading: Answering 70% or more correctly will give you 100% for the WeBwork assginment. Below 70% will be your total number of correct problems divide by 70% of the total number of problems. For example if there are 200 problems and you got 68% or 136 of them correct then your WeBwork score will be out of 70% of 200 or 140, i.e. 136/140 = 97%. This will be added into the Sakai gradebook under the category Homework (15%). Any problem with technical issue will be removed altogether from the calculations.


         Week   Events Resources/Practice Section/Notes Video
Not Graded
Online Homework
Due Date
(by 11:55pm)
8 Mar. 23 - Mar. 27 New WeBWork
Compute Matrix Inverse
Practice Inverse
Practice Inverse Answer
Section 2.2
Section 2.3
No Videos
before break
(Section 2.2) 1, 3, 5, 7, 8, 12, 13, 17, 18, 24, 31, 33
(Section 2.3) 1, 3, 7, 8, 9, 13, 15-17, 22
WeBWorK Friday 3/27
8 Mar. 23 - Mar. 27 Project 2
Fri. Mar. 27
Flop cofactor
Practice Det
Practice Det Answers
Section 3.1
Section 3.2
3.1 Video
3.2 Video
(Section 3.1) 1, 3, 5, 9, 11, 13, 20, 21, 25, 33-36
(Section 3.2) 3, 5, 9, 11, 13, 15, 23 , 25, 31
WeBWorK Monday 3/30
9 Mar. 30 - Apr. 3 Exam 2 (Chapters 2 and 3 and 6.1)
12:00am April 1 to 11:55pm April 3.
Exam 2 Review
Exam 2 Review Answers
Compute Eigenvalues
Practice Eig
Practice Eig Answers
Practice Eig Diag
Practice Eig Diag Answers
Eig - Relates - Poly
Section 5.1
Section 5.2
5.1 Video
5.2 Video
(Section 5.1) 1, 3, 5, 7, 9, 13, 17, 19, 25, 26, 38
(Section 5.2) 1, 3, 7, 9, 10, 15, 18, 23
WeBWorK Monday 4/6
10 Apr. 6 - Apr. 10   Example 4
Subspace Practice
Section 5.3
Section 4.1
5.3 Video
4.1 Video
(Section 5.3) 1, 3, 9, 13, 18, 27, 31
(Section 4.1) 1, 3, 7, 9, 13, 17, 21, 23, 24
WeBWorK Monday 4/13
11 Apr. 13 - Apr. 17     Section 4.2
Section 4.3
4.2 Video
4.3 Video
(Section 4.2) 1, 3, 5, 7, 10, 17, 19, 23, 27
(Section 4.3) 1, 3, 5, 9, 11, 15, 19, 23, 24, 37
WeBWorK Monday 4/20
12 Apr. 20 - Apr. 24 Project 3
Fri. Apr. 24
  Section 4.5
Section 4.6
4.5 Video
4.6 Video
(Section 4.5) 1, 3, 5, 7, 11, 13, 17, 21, 22
(Section 4.6) 1, 3, 5, 7, 11, 25, 26, 31
WeBWorK Monday 4/27
Date/Time: TBA     Exam 3 (Chapters 4 and 5) Exam 3 Canceled.
15 Date/Time: Available: 12:00am Monday May 4 to 11:55pm Friday May 8 Final Exam (Chapters 1, 2, 3, 4, 5, and 6.1) Time limit will be 5 hours. The Final Exam will be 50 multiple choice questions and you will have two attempts on the final exam. The best score will be recorded.