MATH 3100, Section 103 Linear Algebra & Matrix Theory- Spring 2021


  • Ahmed Kaffel
  • Email: ahmed.kaffel (at)
  • Office: Cudahy 360
  • Office hours: MW 3:00-4:00 pm or by appointment


  • MWF 12:00PM–12:50PM Distance learning

Course Description and Learning Objectives:

Covers systems of linear equation, algebra of matrices, linear transformations, determinants, N-dimensional vector spaces, inner product spaces, eigenvalues and eigenvectors, diagonalization and orthogonality, characteristic values, special matrices and applications to differential equations and geometry.
Upon successful completion of the course, students will be able to:
1. Find solutions of systems of linear equations by using Gauss-Jordan elimination method.
2. Identify and compute algebraic properties of matrices and determinants.
3. Demonstrate a thorough knowledge of vector spaces and subspaces.
4. Find basis and rank for column, row and null spaces of a given matrix.
5. Find eigenvalues, eigenvectors and eigenspace of a square matrix and use them for matrix diagonalization.
6. Define linear transformations and examine their properties.
7. Identify inner product spaces and use Gram-Schmidt orthogonalization process to orthogonalize any given basis.
8. Understand and demonstrate the applications to linear ordinary differential equations and geometry
9. Use MATLAB as a tool to help understand linear algebra and to evaluate problems that would otherwise be too large to do by hand.
10. Determine if a linear system has a unique solution, infinitely many solutions, or no solution. 11.
Perform fundamental matrix operations.
12. Determine if a set forms a subspace, a vector space, a spanning set.
13. Determine the linear independence/dependence of a variety of sets.
14. Find bases for different spaces; determine the dimension and rank of the space.
15. Find the inverse of a matrix, if one exists.
16. Perform the LU decomposition.
17. Compute the determinant of a matrix.
18. Determine when a matrix A is diagonalizable.


MATH 2100, MATH 2105, MATH 2350, or MATH 2451.


Introduction to Linear Algebra with Applications, Jim DeFranza & Daniel Gagliardi, McGraw-Hill, ISBN 13: 978-1-4786-2777-7.

Any additional material will be shared via Marquette University’s Course Management System ( Some notes will be shared for the course. These notes should only be used as a supplement and not as an alternative to your personal notes. The instructor will help you to understand the material taught in the lectures and will also help you by doing some review problems before the exams. It is very important that you practice these examples.


There will be two midterm exams and a final exam:
  • 1st midterm exam: Friday, March 5, 2021
  • 2nd midterm exam: Friday, April 16, 2021
  • Final exam: Thursday 05/13/2021 from 10:30AM - 12:30PM
The exam problems are based on the lectures, the textbook, homework problems, and activities. An absence from an exam is recorded as a score of 0. Makeup exams are generally allowed only for university-excused absences. See "Attendance Policy" below. If you feel that your situation warrants a makeup exam, please check with me as soon as possible to request one. Further documentation of your absence may be required. Make-up exams will not be given unless there are extreme circumstances and you inform me of the absence within 48 hours of the exam. You are responsible for scheduling your make-up exam.

Grading policy and Evaluation Criteria:
Your final grade will be determined as follows:
  • Online quizzes: 30%
  • Midterm exams: 20% each
  • Final exam: 30%
Your total score is calculated based on this formula:
Total score= 0.3*quiz score+0.2* exam1 score+0.2*exam2 sore+ 0.3*final exam score.
Your minimum final grade will be A, A-, B+, B, B-, C+, C, C-, D+, and D for course averages of 93%, 90%, 86%, 81%, 76%. 72%, 68%, 64%, 60% and 56%. Grades for assignments and exams will be posted on D2L. Please check your recorded grades regularly to monitor your progress in the course and to ensure accuracy of recorded grades.

Grade Corrections: : If you believe that an exam or a quiz was graded or tallied incorrectly you may submit the exam or the quiz for a regrade along with explaining why you believe you deserve more points. Regrades will be accepted up to two class periods after the exam or the quiz grade is posted. You must let me know (in writing; email is fine) within seven days of receiving the grade; otherwise, I can't promise that I will consider the issue.

Homework assignments:
will be assigned but will not be graded. I strongly recommend neatly writing up solutions to the homework and saving these solutions. These solutions will be a valuable resource when you come to office hours or review for an exam. Problems like the homework will appear on quizzes and exams.
In order to master the material of the course, it is key that you do your homework. You should make every effort to solve the assigned problems using the concepts learned from the lectures and readings. If you have not practiced the techniques within the homework problems, you will have serious difficulties to work problems on exams.

Online quizzes:
Online quizzes will make up 30% of your final grade. We will generally have one or two online quizzes for each chapter which will be posted on D2L. There will be no make-up quizzes unless for sudden medical emergencies until proven. The lowest quiz score (including any ‘0’ for absences) will be dropped. Unless explicitly stated, calculators and notes will not be allowed on quizzes.

Midterm exams:
There will be two in–class exams: Exam 1 will be given on Friday 03/05/2021, exam 2 will be given on Friday 04/16/2021 and each exam is counted 20% toward the final grade. There will be no makeup exams unless for sudden medical emergencies.

Final exam:
There will be a comprehensive final exam grade will be counted as 30% of your final grade. The final exam will be on Thursday 05/13/2021 from 10:30AM - 12:30PM.

Important dates:
Exam 1 date: Friday, 03/05/2021
Exam 2 date: Friday, 04/16/2021
Final exam date: Thursday 05/13/2021 from 10:30AM - 12:30PM.
Classes resume: Jan 25, 2021
Classes end: May 8, 2021

Attendance Policy:
Attendance is required and will be recorded. Attendance is essential to succeed in this course. Missing class almost always results in poorer performance on exams and homework. By attending lectures you will get a sense of what I consider important and that should help you know what to focus on when you study for the exams. You are responsible for lecture notes, any course material handed out, and announcements made in class. You are expected to arrive in class on time with the appropriate lecture notes for the class, having completed the assigned reading for the current lecture and assigned problems for the previous lecture. You are expected to stay through the entire lecture, be prepared to ask questions, and be willing to learn mathematics. If you have a good reason to miss a class, please inform the instructor as soon as possible (preferably via email) to mitigate penalties. The university attendance policy considers more than 6 absences in a 3-credit course to be excessive. With 7 absences you may be dropped from the class. Note that with very few exceptions, the University does not make a distinction between excused and unexcused absences. If you miss a class, it is your responsibility to obtain and learn the material you missed. In the event that you miss a class you should get the material you missed (e.g., from another student) and make an attempt to learn it yourself (or with a tutor). I will also be happy to answer your questions about the missed class. The attendance policy of this course follows the College of Arts and Sciences policy in the Undergraduate Bulletin.

Days off:
- Tuesday, Feb. 9, 2021
- Wednesday, March 10, 2021
- Tuesday, April 20, 2021
- Wednesday, May 5, 2021

Class participation and active learning are important aspects of this class, so your engagement is critical to your success regardless of modality/delivery. However, I understand that sometimes you must miss examinations or other academic obligations affecting your grades because of illness, personal crises, and other emergencies. As long as such absences are not excessive (no more than a total of 8 absences per semester), I will work with you as best I can to help you succeed in the course. Please contact me as soon as possible when such absences arise so we can make arrangements to get you caught up. This policy will not apply in the case on non-emergency absences. All students who participate in class will receive extra credit points for (correctly) answering specific extra credit questions. Do not miss this opportunity to improve your grade.

Technology Requirements:
To be successful in this course, you will need to have foundational experience with D2L, the University’s Learning Management System, and the videoconferencing tool Microsoft Teams. If you’re not familiar with these technologies, review the D2L Student Help resources and Students Use Microsoft Teams for online/live classes webpage. I recommend you also visit the Technology for Remote Learning webpage for information on the technology you will need to be successful. For general questions about technology, contact the ITS Help Desk at or 414-288-7799.

Ethics and Behavior:
High standards of personal conduct and consideration of others are required in order to create a classroom climate conductive to learning. Disruptive behavior will not be tolerated.

Norms for classroom conduct are based on respect for the instructor and the fellow students. Behavior such as texting, updating social media, playing games, or otherwise distracting fellow students is inappropriate.

Academic Support:
It is your responsibility to keep abreast of the course, to master the material covered, and to take the initiative for getting the help you need. You are encouraged to obtain help from the course instructor. However, if you miss a class, you are responsible for the missed materials. The MUSC Tutorial Program offers tutorial. For more information see the MUSG website at .

If you have a disability and require accommodations, please contact me early in the semester so that your learning needs may be appropriately met. You will need to provide documentation of your disability to the Office of Disability Services. If you are unsure of what you need to qualify for services, visit the Office of Disability Service's website or call the Office of Disability Services at 414-288-1645. The office of Disability Services is also prepared to help students process accommodation requests based on medical or personal needs related to COVID-19. Please contact as soon as possible if you feel you may need to explore modifications related to a disability or COVID-19, even if that need may not be immediate.

Communication standards:
Marquette University’s policy on email: “E-mail is an appropriate and preferred method for official communication by Marquette with students unless otherwise prohibited by law. The university has the right to send official communication to students by e-mail with the assumption that students will receive, read and, if necessary, act in a timely manner based upon these e-mails.” If I need to contact you outside of class, I will use your Marquette email address, and expect that you will read and respond to this communication in a timely manner. Additionally, please recognize standard email etiquette. Initial emails to me should contain (minimally) a subject, greeting and closing. I will attempt to respond to students within 24 hours. If you have not received a reply from me within 24 hours, please resend the email. Since this is a fully online course, your communications with me and other students are critical to your learning experience. Please be respectful to others as you communicate. In addition to Netiquette at Marquette policy, I would like to ask you to be cautious of dominating any discussion, keep an open mind and be sure to proof read and edit prior to publishing anything to D2L.

Subject to Change Clause:
This syllabus is subject to change at the discretion of the instructor to accommodate instructional and/or student needs. Such change will be announced to the class at the appropriate time.

Course Schedule

The table below lists the main textbook sections and topics to be covered in class.

Chapter #

Textbook sections and topics


1.1 Systems of Linear Equations
1.2 Matrices & Elementary Row Operations
1.3 Matrix Algebra
1.4 The Inverse of a Square Matrix
1.5 Matrix Equations
1.6 Determinants
1.7 Elementary Matrices & LU Factorization Periodic Functions


2.1 Vectors
2.2 Linear Combinations
2.3 Linear Independence


3.1 Vector Spaces
3.2 Subspaces


4.1 Linear Transformations
4.2 The Null Space and Range
4.4 Matrix Representation of a Linear Transformation


5.1 Eigenvalues & Eigenvectors
5.2 Diagonalization


6.1 The Dot Product
6.3 Gram-Schmit Process

Supplement notes and slides:

Slide1 Slide2 Slide3 Slide4 Slide5 Slide6 Slide7 Slide8 Slide9 Slide10 Slide11 Slide12

Note all the slides and notes are uploaded on D2L under content


Thursday, February 18 : All the notes and slides are uploaded on D2L.

Monday, January 25 : Welcome to Math 5510! I wish you all the best for this spring term.