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COURSE OUTLINE
Toronto Metropolitan University (TMU)
MTH141, Linear Algebra
Fall 2022
INSTRUCTORS:
• The course coordinator of this course is K. Lan; Website: https://math.ryerson.ca/∼klan/
Instructor
Office
Tel. ext.
Email
Officehours
K. Lan
ENG229
556962
klan@ryerson.ca
Wed. 2:00- 4:00pm
S. Samiezadeh
VIC 703
553811
saeid.samiezadeh@ryerson.ca
Thur. 10:30-11:30am
M. Alqasas
VIC 703
553811
malqasas@ryerson.ca
Fri. 10:00-12:00pm
C. Wang
VIC 703
553811
cpwang@ryerson.ca
Thur 12:30 – 2:00pm
A. Sayyidmousavi
VIC 703
553811
asayyidmousavi@ryerson.ca
Thur. 12:00-2:00pm
• Office hours take place in the instructor’s office. The instructors are available at these times and at other
times by appointment for individual assistance and consultation.
Email Policy
Students are expected to monitor and retrieve messages and information issued to them on a frequent
basis. All official or formal electronic communications from students must be sent from their official TMU
Email account. Emails from other addresses may not be responded to. You would write down the course
number and your section number in your emails.
Calendar Course Description
Systems of linear equations and matrices. Determinants. Vector spaces. Inner product spaces. Eigenvalues and eigenvectors. (see https://www.torontomu.ca/calendar/2022-2023/courses/mathematics/MTH/141/)
Lecture time and locations
Instructor
Section
Lecture-Time and
Locations
K. Lan
1 − 6, 30
Thur, 8-10am, LIB072
Fri, 8-10am, LIB072
S. Samiezadeh
7 − 12
Thur, 8-10am, DSQ02
Fri, 8-10am, DSQ02
M. Alqasas
13 − 18
Thur, 8-10am, DSQ03
Fri, 8-10am, DSQ03
C. Wang
19 − 24
Mon, 9-11am, DSQ03
Fri, 8-10am, DSQ12
A. Sayyidmousavi
25 − 29
Wed, 8-10am, DSQ02
Fri, 8-10am, DSQ24
Fall Study Week: October 10-14, 2022. There will be lectures during this week except Thanksgiving on
Monday, October 10.
1
MATH Labs: Labs will begin from the second week (starting on the week of September 12, 2022 and
ending on the week of November 28, 2022). There will be no labs during September 6-9, 2022.
TAs and Labs
Sec
Time and location
TA
Email
1
Mon.,8:00-9:00am, VIC106
S. Dayasthasan
dayasthasan.sinnathu@ryerson.ca
2
Fri,12:00-13:00pm, SHE652
Shahab Ghorbani
sghorbani@ryerson.ca
3
Tue,10:00-11:00am, SHE651
Vivija You
vyou@ryerson.ca
4
Mon,13:00-14:00pm, SHE554
Shubham Kundu
shubham.kundu@mail.utoronto.ca
5
Fri,14:00-15:00pm, ENGLG13
Pengfei Wu
pengfei.wu@ryerson.ca
6
Wed,10:00-11:00am,SHE549
Bushra Raja
bushra.raja@ryerson.ca
7
Mon,14:00-15:00pm, EPH111
Shubham Kundu
shubham.kundu@mail.utoronto.ca
8
Wed,13:00-14:00pm,POD367
Holden Pimentel
holden.milne@gmail.com
9
Fri,12:00-13:00pm, VIC200
Phuc Ngo
phuc.ngo@ryerson.ca
10
Fri,15:00-16:00pm, EPH204
K.Kanapathyshan
kanapathyshan.krishn@ryerson.ca
11
Tue,11:00-12:00pm, SHE651
Phuc Ngo
phuc.ngo@ryerson.ca
12
Fri,14:00-15:00pm, POD366
K.Kanapathyshan
kanapathyshan.krishn@ryerson.ca
13
Mon,15:00-16:00pm, VIC106
Sijiao Liu
sijiao.liu@ryerson.ca
14
Tue,12:00-13:00pm,EPH111
Shuang Liang
shuangliang660@gmail.com
15
Mon,13:00-14:00pm, TRS1075
Gustavo Cicchini
gcicchinisantos@ryerson.ca
16
Tue,10:00-11:00am, VIC305
M.Khatami
m1khatami@ryerson.ca
17
Wed,15:00-16:00pm,POD367
Lazar Mandic
lazar.mandic@ryerson.ca
18
Thur,17:00-18:00pm,SHE651
Dedan Deus
dedan.deus@aims.ac.rw
19
Wed,14:00-15:00pm,SHE651
Lazar Mandic
lazar.mandic@ryerson.ca
20
Tue,11:00-12:00pm,SHE660
Vivija You
vyou@ryerson.ca
21
Fri,12:00-13:00pm, SHE549
Naeimeh Atabaki
naeimeh.atabaki@gmail.com
22
Fri,13:00-14:00pm, SHE598
Pengfei Wu
pengfei.wu@ryerson.ca
23
Tue,14:00-15:00pm,SHE652
Shuang Liang
shuangliang660@gmail.com
24
Wed,10:00-11:00am,EPH111
Holden Pimentel
holden.milne@gmail.com
25
Fri,13:00-14:00pm, SHE549
Dedan Deus
dedan.deus@aims.ac.rw
26
Mon,14:00-15:00pm, SHE554
Gustavo Cicchini
gcicchinisantos@ryerson.ca
27
Tue,14:00-15:00pm,VIC303
Areebah Muhammad
areebah.muhammad@ryerson.ca
28
Wed,14:00-15:00pm,TRS2164
Bushra Raja
bushra.raja@ryerson.ca
29
Tue,15:00-16:00pm,VIC200
Areebah Muhammad
areebah.muhammad@ryerson.ca
30
Tue,10:00-11:00am, EPH111
Shahab Ghorbani
sghorbani@ryerson.ca
Note that Section i=Section i1 (lecture)=Section i2(Lab), where i = 1, 2, for example,
Section 1=Section 011 (lecture)=Section 012(Lab).
2
Print text and eTEXT:
Linear Algebra by Kunquan Lan (fourth edition), Pearson, 2020.
Print text: ISBN: 9780136800309
You can buy the print text from TMU campus store.
Digital Option Only: Purchase access code 9780137889181 from TMU Campus Store. Redeem access
code at http://www.pearsoncustom.com/can/ryerson mth108.
Note: 9780137889181 is the ISBN for the access code. Students need to purchase 9780137889181 from the
TMU Campus Store website. Once they make their purchase they will be emailed their access code which
they can then redeem at the website: http://www.pearsoncustom.com/can/ryerson mth108.
Note that you may need to retype the underscore
in the above link if it doesn’t work.
1. Go to https://campusstore.ryerson.ca/topic/accesscodes.
2. In the search box at the bottom of this above website page, click MTH141 (Fall 2022) and then click
search. There are instructions on how to buy the access code on this page.
3. Once students make their purchase, they will be emailed their access codes.
4. Then students can go to the website: http://www.pearsoncustom.com/can/torontometro math108 to
redeem for the etext.
Course Objectives:
1. To gain a facility with the basic concepts and techniques of linear algebra.
2. To build a strong foundation in linear algebra as preparation for subsequent courses in mathematics,
science and engineering.
3. To nurture abilities in analytic and creative thinking and problem-solving.
Syllabus: We shall study the following sections:
Chapter 1: Euclidean spaces, section 1.1-1.4
Chapter 2: Matrices, sections 2.1-2.5, 2.7, Skip 2.6
Chapter 3: Determinants, sections 3.1-3.4; Skip Theorem 3.3.7, Example 3.3.9 and exercise 4.
Chapter 4: Systems of linear equations, sections 4.1-4.6
Chapter 5: Linear transformations, sections 5.1-5.3
Chapter 6: Planes and lines in R3 , sections 6.1-6.3
Chapter 7: Bases and dimensions, sections 7.1
Chapter 8: Eigenvalues and diagonalizability, sections 8.1-8.2
Chapter 9: Vector spaces, sections 9.1-9.2
Chapter 10: Complex numbers, sections 10.1-10.4
3
Topics and Course Schedule
Week
Date
Activity
Sections
1
Sept6 − 9
Lecture
1.1-1.2
2
Sept12 − 16
Lecture
1.2-1.4, 2.1, 2.2
3
Sept19 − 23
Lecture
2.3, 2.4, 2.5
4
Sept26 − 30
Lecture
2.7, 3.1, 3.2, 3.3
5
Oct3 − 7
Lecture
3.4, 4.1, 4.2
6
Oct10 − 14
Lecture,Midterm
4.3, 4.4
7
Oct17 − 21
Lecture
4.5, 5.1,5.2
8
Oct24 − 28
Lecture
5.3, 6.1,6.2
9
Oct31 − Nov4
Lecture
6.3, 7.1
10
Nov7 − 11
Lecture
8.1, 8.2
11
Nov14 − 18
Lecture
8.2, 9.1,9.2
12
Nov21 − 25
Lecture
9.2, 10.1,10.2
13
Nov 28 − Dec2
Lecture
10.3,10.4
Note that we will not cover all the sections in some chapters.
Homework and Quizzes:
A number of homework questions listed at the end of the course outline are assigned every week and
available from the D2L after the end of each week’s lecture. Please note that the assignments will not be
marked; however, they may be checked for completeness and correctness. Experience has shown that the
only way to learn math is to do it. The amount you learn in this course and the grade you receive will be
proportional to the amount of time you spend doing problems. Keep up with the homework. Each student
should do at least 4 hours of independent study after 4 hour lectures each week.
• Each homework and quiz problems are from the material we studied in last week’s lecture.
• You need to hand in each homework to the Assignment in Assessment in D2L by 11:59pm, every
Friday, starting on September 16 and ending at Dec 2.
• Assistance with mathematical questions on the course or homework is available at the Math Lab.
• There will be a weekly 15 minutes quiz at each lab with problems analogous to the assigned homework
problems or examples given in class. Each quiz must be submitted to your TA before the deadline assigned
by your TA during the lab. You will get zero marks for the quiz if you submit your quiz late.
• Each quiz must be written in your own section. If you write it in another section, you will get zero
marks for the quiz.
• Full solutions to each quiz will be given by your TA in the next Lab.
• Last lab ends in the week of November 28, 2022.
• There will be no make-up quiz whatever reasons you provide.
4
• You can hand in your missing homework to your TA after you submit suitable documents (see Missed
Class and/or Evaluations below) to your department and get permission from your MTH141 instructor.
Quiz, HW
Date of lecture
submission by 11:59pm
Sections
1
Sept6 − 9
Sept 16
1.1-1.2
2
Sept12 − 16
Sept23
1.2-1.4, 2.1, 2.2
3
Sept19 − 23
Sept30
2.3, 2.4, 2.5
4
Sept26 − 30
Oct7
2.7, 3.1, 3.2, 3.3
5
Oct3 − 7
Oct14
3.4, 4.1, 4.2
6
Oct10 − 14
Oct21
4.3, 4.4
7
Oct17 − 21
Oct28
4.5, 5.1,5.2
8
Oct24 − 28
Nov4
5.3, 6.1,6.2
9
Oct31 − Nov4
Nov11
6.3, 7.1
10
Nov7 − 11
Nov18
8.1, 8.2
11
Nov14 − 18
Nov25
8.2, 9.1,9.2
12
Nov21 − 25
Dec2
9.2, 10.1,10.2
13
Nov 28 − Dec2
10.3,10.4
Evaluation:
ˆ 10%: You must hand in the weekly assigned homework to the Assignment in Assessment in D2L by
11:59pm, every Friday, starting September 16 in order to receive 10% of the final grade.
ˆ Quizzes (12%): There will be a 15-minute quiz during every lab, starting in the week of September 12,
2022.
ˆ Midterm (36%): 1.5 hours; 8:10-9:40am, Friday, October 14, 2022.
ˆ Final Exam (42%): 2 hours, during the examination period: December, 2022.
Format:
The formats of the midterm and final exam are both multiple choice and full-answer problems.
Aids: You are NOT allowed to use any AIDS including calculators, formula sheets, scrap paper and cell
phones during the weekly quiz, midterm test or final exam for this course.
NOTE:
• You must bring a TMU Photo ID to the weekly quiz, the midterm and the final exam.
• You must use the pencils to fill in the scantron sheets for the multiple choice questions.
Re-marking of Test If a test is submitted for re-marking, the whole test may be remarked.
5
Missed Class and/or Evaluations
1. Students are required to inform their instructors of any situation which arises during the semester which
may have an adverse effect upon their academic performance, and must request any considerations and
accommodations according to the relevant policies and well in advance. Failure to do so will jeopardize
any academic appeals.
2. If a test is missed, then the corresponding percentage of the test will be transferred to the final exam
or write a make-up test. If the final exam is missed, an INC grade may be given, in accordance to
the policies given in https://www.ryerson.ca/senate/course-outline-policies/missed-tests-examinationscourse-management-policy-166/.
3. If proper documentation is not received by the instructor within reasonable time (generally, that means
within 3 working days), the mark for the missed evaluation will be zero.
Medical Certificates
If a student misses the deadline for submitting an assignment, or the date of an exam or other evaluation
component because of illness, they must submit a TMU Student Medical Certificate AND an Academic
Consideration form within 3 working days of the missed date. Both documents are available at (PDF)
Student Medical Certificate Guidelines (https://www.ryerson.ca/content/dam/senate/forms/medical.pdf).
You must submit your forms to your own program department.
Religious Observance
If a student needs accommodation because of religious observance, they must submit a Request for
Accommodation of Student Religious, Aboriginal and Spiritual Observance AND an Academic Consideration
form within the first 2 weeks of the class or, for a final examination, within 2 weeks of the posting of
the examination schedule. If the required absence occurs within the first 2 weeks of classes, or the dates
are not known well in advance as they are linked to other conditions, these forms should be submitted
with as much lead time as possible in advance of the required absence. Both documents are available
at (PDF) Student Request for Accommodation of Student Religious, Aboriginal and Spiritual Observance
(https://www.ryerson.ca/senate/forms/relobservforminstr.pdf). If you are a full-time or part-time degree
student, then you must submit the forms to your own program department or school.
Students who need Academic Accommodation Support
Students who need academic accommodation support should register with Academic Accommodation
Support (https://www.ryerson.ca/studentlearningsupport/academic-accommodation-support/). Before the
first graded work is due, registered students should inform their instructors through an ”Accommodation
Form for Professors” that they are registered with Academic Accommodation Support and what accommodations are required.
6
Academic Integrity and Plagiarism
TMU’s Academic Integrity Policy applies to all students at the University. The policy and its procedures
are triggered in the event that there is a suspicion that a student has engaged in a form of academic
misconduct. Forms of academic misconduct include plagiarism, cheating, supplying false information to the
University, and other acts. The most common form of academic misconduct is plagiarism. Plagiarism is a
serious academic offence and penalties can be severe. In any academic exercise, plagiarism occurs when one
offers as one’s own work the words, data, ideas, arguments, calculations, designs or productions of another
without appropriate attribution or when one allows one’s work to be copied. All academic work must be
submitted using the citation style approved by the instructor. Students may refer to the TMU Library’s list
of Citations and Style Guides (https://library.ryerson.ca/guides/style/) for more information.
It is assumed that all examinations and work submitted for evaluation and course credit will be the
product of individual effort, except in the case of group projects arranged for and approved by the course
instructor. Submitting the same work to more than one course, without instructor approval, is also considered
a form of plagiarism. Students are advised that suspicions of academic misconduct may be referred to the
Academic Integrity Office (AIO). Students who are found to have committed academic misconduct will have
a Disciplinary Notation (DN) placed on their academic record (not on their transcript) and will be assigned
one or more of the following penalties:
• A grade reduction for the work including a grade of zero for the work.
• An F in the course.
• More serious penalties up to and including expulsion from the University. For more detailed information on these issues, please refer to the full online text for the (PDF) Academic Integrity Policy
(https://www.ryerson.ca/content/dam/senate/policies/pol60.pdf) and to the Academic Integrity website
(https://www.ryerson.ca/academicintegrity/).
Important Resources Available at TMU
• The Library (https://library.ryerson.ca/) provides research workshops and individual assistance. Inquire at the Reference Desk on the second floor of the library, or go to Research Skills Workshops
(https://library.ryerson.ca/info/workshops).
• Student Learning Support (https://www.ryerson.ca/studentlearningsupport/) offers group-based and
individual help with writing, math, study skills and transition support, and other issues.
• For more resources and information on significant dates, academic standings, exam schedules, etc., visit
the Current Students website (https://www.ryerson.ca/current-students/).
• The Student Guide (https://www.ryerson.ca/studentguide/) summarizes the policies, fees, procedures
and services you’ll need to know as a Ryerson student.
Copyright
The Pearson publisher owns the copyright of the etext. You are not allowed to download the etext and
pass it onto anyone else, or distribute it commercially.
7
Homework for Linear Algebra Weekly homework questions corresponding to the material you have
studied in the week will be posted to D2L by the instructor. You need to hand each homework to the
corresponding homework submission fold in the Assignment in Assessment in D2L by 11:59pm, every
Friday, starting on September 16.
In the following table, the first column lists the sections we shall study; the second one lists the Definitions
which you need to understand; the third column lists theoretical results including Theorems, corollaries and
propositions. We do not teach the proofs of these theorems, corollaries and propositions in general, but
you have to understand the theoretical results and know how to apply them. These can be learnt from the
instructors in her/his lecturing and via studying the text-book and doing the homework. In the midterm and
the final exam, there will be some thinking problems which you need to use the knowledge of these theoretical
results. The fourth column lists examples you need to study by applying the definitions, theorems, corollaries
or propositions. The last column lists the homework questions which you need to hand in. You can do all
other exercise questions of each section. The full solution to each question can be found in the Appendix of
the textbook.
8
Sec
Definition
Theorem
Example
Questions to be handed in
1.1
1−7
1−2
1−8
3, 5, 6, 7, 10, 12, 13(2), 15, 17, 18
1.2
1−5
1−8
1−9
1(ii), 2(ii), 3A, B, 4(iii), 6(5), 7; 8(iv), (v);
9(i), (iii); 10(i); 11, 12
1.3
1
1 − 2, Cor.1(2)
1−3
1(3), (4); 2; 5(4), (6); 6(b), (c)
1.4
1
1−3
1−6
1(1); 3; 4(2); 5
2.1
1−4
1
1 − 10
7; 10(3); 11
2.2
1−2
1−3
1 − 10
1, 7, 11, 12
2.3
1
1
1−7
1A3 ; 2, A4 , 3, 4, 5
2.4
1
1
1 − 12
1, D, H, 2, C, E, 5C, 6, A, F
2.5
1−2
1−5
1−3
1A, C
2.7
1
1, 4 − 9, Cor.1
1−6
1; 2; 3B, C; 4, 5; 6A; 7D, E;
3.1
1
1−3
1−5
1; 2A1 ; 3|A|; 4
3.2
1−2
1−3
1−3
1A; 2|B|; 3; 4|D|, |F |
3.3
1 − 3, Cor.1
1−7
1|A|; 2|A|, |F |, 3|A|
3.4
1−4
1−5
1A, C, E; 2.2A, B; 3(5), (6); 4.
1
1−8
1(d); 2(2); 3; 4(a); 5.
1
1−5
1(i); 2(a), (c), (e)
1−2
1a), e), h), 2a), c), e)
4.1
1−3
4.2
4.3
4.4
1 − 2, Cor.1
1−4
1a), d); 2, 3, 4a), d)
4.5
1 − 5, Cor.1-3
1−5
1c); 2a), 3a); 4, 5, 6, 7
4.6
1−2
1−6
1, 2, 5
5.1
1−3
1, Prop.1
1−6
1A3, 2, 3, 4a), 5, 7, 8, 9b)
5.2
1−3
1−5
1−4
1a); 2; 3c); 4c)
1 − 5, 6(1) − (3)
1−6
1, 2, 3(2), 4, 6
5.3
6.1
1
1−2
1−2
1(4), 2, 3, 4(1).
6.2
1−2
1, 3
1, 2, 4
1, 4
6.3
1−5
1 − 5, Prop.1
1 − 11
1(a), 2(a), 3(a), 4, 5, 6(a), 7, 8(a), 9 − 13,
14(a), 15(a)
7.1
1
1 − 5, Cor.1,2
1−5
1−4
8.1
1−3
1, 3, 4, 5, Cor.1
1−6
1(B), 2(B), (D), 3, 4
8.2
1
1, 2, 6, Cor.1
1−5
1(B), 2, 3, 4, 8; 5, 6, 7
9.1
1−3
1, 3, 4, 5, Cor.1
1−6
1, 2, 4, 7, 8, 12
9.2
1
1, 2, 6, Cor.1
1−5
1, 2, 3, 4, 5
10.1
1−5
Prop.1,2
1−9
1−9
10.2
1, 2
1, 2
1−3
1, 2
10.3
1, 3, Cor.1
1, 5
10.4
1, Cor.1
1−3
9
1−4
1, 2