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Winter 2022: MAT A22 Linear Algebra I for Mathematical Sciences

MAT A22 Graphic Syllabus

From the Course Calendar:

“A conceptual and rigorous approach to introductory linear algebra that focuses on mathematical proofs, the logical development of fundamental structures, and essential computational techniques. This course covers complex numbers, vectors in Euclidean $n$-space, systems of linear equations, matrices and matrix algebra, Gaussian reduction, structure theorems for solutions of linear systems, dependence and independence, rank equation, linear transformations of Euclidean $n$-space, determinants, Cramer’s rule, eigenvalues and eigenvectors, characteristic polynomial, and diagonalization.”

This course leads up to MAT B24 Linear Algebra II:

“Fields, vector spaces over a field, linear transformations; inner product spaces, coordinatization and change of basis; diagonalizability, orthogonal transformations, invariant subspaces, Cayley-Hamilton theorem; hermitian inner product, normal, self-adjoint and unitary operations. Some applications such as the method of least squares and introduction to coding theory.”

Course Coordinator’s Message

I’m glad that you’re taking this course. It is a really special course, because linear algebra powers everything from Google’s PageRank algorithm to the shading of pixels in video games. Moreover, this course in linear algebra introduces you to mathematics proofs in context. Linear algebra has some of the nicest or cleanest proofs in mathematics. It is the model of a nice simple theory with surprisingly powerful applications.

This course leads to MAT B24 and also deep ideas from MAT C01. It is the beginning of your journey in to algebra. I love linear algebra because it is magic that works. I hope that in this course you’ll experience some of the joy and wonder that this subject contains.

Policy on In-Person vs Online Delivery

We are making every effort to provide an in-person educational experience. The Ontario government has asked us to remain online until January 31st. That means, we’ll be online for at least the first three weeks of classes. We are planning to have in-person midterms and an in-person exam. However, we recognize the threat posed by omicron variant of COVID-19. As we get more information from the Registrar and the Ontario government, we will keep you updated and informed.

Currently, we plan for:

Activity Mode of Delivery
Lecture Online until January 31st, and in-person afterwards
Tutorial Online until January 31st, and in-person afterwards
Term Tests In-person with dates to be announced
Exam In-person with date to be announced

Frequently Asked Questions

Course Staff


Communication Policy


This term we will be using Piazza for class discussion. The system is highly catered to getting you help fast and efficiently from classmates, the TAs, and myself. Rather than emailing questions to the teaching staff, I encourage you to post your questions on Piazza. If you have any problems or feedback for the developers, email

Find our class signup link at:


Please include your name and student number in every e-mail that you send. Mail must be from an official University of Toronto account. To make sure that your e-mail does not get lost you must include this magic formula in the body:


Be sure to include the precise question, and the problem or difficulty. If you’re not able to write out the question, take a photo or attach a PDF.

Above all, don’t worry about e-mailing me or any of the course staff. We are not evil trolls. We won’t get angry if you e-mail us. Answering student e-mails is a part of our job.

However, e-mail is only part of our job. We might not respond to your e-mail on the same day that you send it. Generally, give us at least two business days to respond. Parker has limited access to his computer on Tuesdays, Thursdays, and weekends.

Here is an example of a well-formatted e-mail:

 Subject: [MAT A22] What is a vector?
 Hi! I am Leonhard Euler (12932188) from MAT A22.
 I need help with this question: Find a vector orthogonal to (1,1).
 My problem is this: I don’t know what the word "vector" means.

All e-mails must include the following:


We are going to use two books for this course, both of them are free online.

Primary book: Linear Algebra with Applications by Keith Nicholson. This is a book with lots of computations and examples. It is suitable for MAT A23 or MAT A22. We will use it as the primary reference for the course, and follow its notation and section order.

Secondary book: Linear Algebra Done Right by Sheldon Axler. This is a formal and proof oriented introduction to linear algebra. We will use it as a reference, and will sometimes use it as a source of homework problems.

Grading Scheme

Task Weight
Exam 40%
Term Tests 2x20%
Assignments (6-1)x4%


Goal: these assignments give you the opportunity to deepen your understanding of topics covered in this course, and to practice. We use these assignments to determine if you can solve problems slowly, without time constraints.

Procedure: we will be using Crowdmark to grade assignment submissions. You will get a personalized submission link sent to your UToronto email address. Do NOT share this link with other students.

Submission Guidelines: Assignments need to be submitted online through Crowdmark. You will have a week to write the assignment.

Evaluation Criteria: The TAs will grade two of the five questions. Present your solutions in a logical and clear manner. Detailed solutions will be made available shortly after the deadline of submission.

Please pay attention to the following when writing assignments:

Common Questions about Assignments

Term Tests

Goal: these written tests give you the opportunity to demonstrate your understanding of core concepts and topics in a written format. You will gain experience of communicating mathematical ideas in a logical manner. We write tests in a limited amount of time to assess your fluency with the material.

Procedure: We will hold term tests outside of class time. We will post an announcement on Quercus about where and when to write the term tests. They will be written in-person and invigilated. You will have two hours to write each test.

Evaluation Criteria: In general, you need to present your solutions in a logical and clear manner. Detailed solutions will be made available shortly after the tests.

Common Questions about Term Tests

Policy on Missed Term Tests

Life is full of unexpected complications. Sometimes, people miss term tests.

If you miss the first term test, then your grading scheme becomes:

Task Weight
Exam 40%
Second Term Test 30%
Homework (6-1)x6%

If you miss the second term test, then your grading scheme becomes:

Task Weight
Exam 40%
First Term Test 20%
Homework (6-1)x8%

If you miss both term tests, then you must meet with Parker to discuss alternatives for you.

How Does Grading Work?

The professors set the assignments and term tests. You, the student, do your best work and hand it in. The TAs then grade your term tests and assignments. Please note, that the professors do not directly look at your homework. The TAs then return your graded work, and you may request a re-grade or further comments if you think the grading is unclear.

For assignment, the TAs will only grade two of the five questions. This policy of subset grading helps us to save time and energy, and teaches you to evaluate your own work.

For term tests, the TAs will grade all the questions.

Common Questions about Grading


You can use the official MAT A22 Re-Grade Form.

All requests will be read and considered by Kaidi Ye and Parker Glynn-Adey. You may submit a regrade request within one-week of receiving your grade. We will make sure that you get a response before the final exam. Submit one copy of this form for each regrade request. If you would like three questions regraded, please submit three copies of this form.

Common Questions about Regrading




Suggested Exercises (Up to Week 6)

Schedule of Tasks

Week Task
2 Assignment 1
4 Assignment 2
6 Assignment 3
Reading Week!
8 Assignment 4
10 Assignment 5
12 Assignment 6

Exact Dates of Tasks

Task Date and Time of Task Date and Time of Solutions
Assignment 1 Monday January 10th at 13:00 to Thursday January 20th at 13:00 Monday January 24th at 12:45
Assignment 2 Monday January 24th at 13:00 to Thursday February 3rd at 13:00 Monday February 7th at 12:45
Assignment 3 Monday February 7th at 13:00 to Thursday February 17th at 13:00 Monday February 21st at 12:45
Assignment 4 Monday February 28th at 13:00 to Thursday March 10th at 13:00 Monday March 14th at 12:45
Assignment 5 Monday March 14th at 13:00 to Thursday March 24th at 13:00 Monday March 28th at 12:45
Assignment 6 Monday March 28th at 13:00 to Thursday April 7th at 13:00 Monday April 11th at 12:45
Term Test 1 will be announced when the Registrar gives us a date
Term Test 2 will be announced when the Registrar gives us a date
Exam will be announced when the Registrar gives us a date

To add the dates above to your Google Calendar, import this calendar.

Academic Integrity

The instructional team wants to make sure that everyone has a fair chance to succeed in this course. Therefore, we define an academic integrity violation to be accessing or communicating with any person or resource that gives a unique advantage to some students. For example: participating in private group chats, posting questions and reading solutions on websites, hiring or requesting external help. All of these would give some students advantages that would not be available to other students.

Common Questions:

References on Academic Integrity

Campus Resources

Facilitated Study Groups

Facilitated Study Groups (FSGs) are weekly drop-in collaborative learning sessions for students who want to improve their understanding of challenging content in selected courses at UTSC. FSG sessions give you a chance to discuss the lecture material and important concepts, develop study strategies and fresh approaches, and work through problems as a group to prepare for your assignments and tests.

Research shows that students who regularly attend FSGs gain a deeper understanding of the material and, on average, achieve better grades. It’s also a great way to meet classmates and study in a relaxed, judgment-free space.

Center for Teaching and Learning Academic Learning Support

The Centre for Teaching and Learning provides academic learning support to students through online tutoring, workshops, and peer supports to drive student success. To find out more about all their offerings, see this website:

Math and Stats Support

The Center for Teaching and Learning’s Math & Statistics Support provides free seminars, workshops, virtual tutoring, individual appointments, and small-group consultations to improve students’ proficiency in various subjects of mathematics and statistics. Their main goal is to create a friendly, vibrant environment in which all students can come to learn and succeed.

For their online help offerings see:


Published: Jan 1, 2022

Last Modified: Jul 8, 2024


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