Math 1B03 - Linear Algebra I
(Fall 2020)

This course is an introduction to linear algebra. We are interested in both a computational approach (e.g., computing solutions to a linear system of equations) and a theoretical approach (e.g., an understanding of the underlying idea of a vector space). The prerequisite for this course is Grade 12 Calculus and Vectors U or MATH 1F03.

News

Schedule

Homework/Quizzes

Handouts

Grading Scheme

Policies

Course Information

There are two sections of Math 1B03 during the Fall 2020 semester. Both sections are identical (they will follow the same schedule, have the same homework, midterms, and final). This webpage is for both sections.

Important Note:

This webpage will be static; the purpose of this webpage is to collect together all of the need resources for the course. All news and changes to the course will will be posted on Avenue-To-Learn.

Instructors:

Section C01: Will Rushworth

Office: Hamilton Hall 319
Office Hours: see website
Email: will.rushworth@math.mcmaster.ca

Section C02: Adam Van Tuyl (Course Coordinator)

Office: Hamilton Hall 419
Office Hours: see website
Email: vantuyl@math.mcmaster.ca

Place and Time: (for all virtual classrooms, use the links in Avenue-to-Learn)

Section C01: Monday, Wednesday 2:30PM-3:20PM Friday 4:30PM-5:20PM in Virtual Classroom
Section C02: Tuesday, Wednesday, Friday 12:30PM-1:20PM in Virtual Classroom
Tutorial T01: We 10:30PM - 11:20PM in Virtual Classroom
Tutorial T02: Tu 11:3APM - 12:20PM in Virtual Classroom
Tutorial T03: We 10:30PM - 11:20PM in Virtual Classroom
Tutorial T04: Tu 11:3APM - 12:20PM in Virtual Classroom

TAs:

Tutorials T01 and T02: TBD

Math Help Center: The Math Help Center will have dedicated TAs for Math 1B03.

Hours: TBD

Textbook:

(Required) Linear Algebra and its Applications 6th Edition
by David C. Lay, Steven R. Lay, Judi J. McDonald
You can purchase or rent a PDF version of this textbook. If you want a hard copy, you need to purchase access to the publishers MyLab, and then purchase the looseleaf version through their website. We will not be using MyLab, so it is not required that you have access to this feature. If you do purchase the version with MyLab, here are:
- Instructions to Access MyLab Version
Here is a link to the book on the campus bookstore website:
- Purchase at Campus Bookstore
(Alternative) You can use the 5th edition of this book. Please note that this book is used in the follow up course Math 2LAS. The 5th edition is missing a chapter used in Math 2LA3, so if you plan on taking Math 2LA3, the 6th edition is recommended.
(Optional) Student Solutions Manual

Important Links:

The following websites will be used during this course:

Avenue to Learn: This is McMaster's learning management system, which will be used to for providing news and updates to students. As well, links to all the video lectures will be provided.
Math 1B03 YouTube Channel: This YouTube channel will contain all the pre-recorded lectues.
ChildsMath: The Math Department's online homework tool. You will use this portal to access homework, labs, and quizzes.
Octave Online: We will use this website to complete our computer labs.

In addition, the following online app on linear algebra may be of interest.

https://www.pocketmath.app

We were contacted by the developers, and we decided that it may help you learn some of the concepts in this class. Try it out and let us know what you think!

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Schedule

We will be using the following schedule. Please note that there may be changes; always refer to Avenue-to-Learn for any updates.

Course Delivery:

The course will be delivered using both asynchronous and synchronous components. The asynchronous component consist of video lectures of the course material (posted on Avenue and YouTube). For the synchronous component, we will use the scheduled class time as follows:

First lecture of the week. (Monday or Tuesday depending on section) The schedule class time will be used as a problem solving session based upon the online lectures of the previous week.
Second lecture of the week. (Wednesday for both sections) There will be an online 20 minute quiz based upon the lectures of the previous week. The quizzes between the two sections will be different, but have the same level of difficulty. The remainder of the scheduled class time can be used to catch up on videos and/or ask your instructors questions. They will be online during this time.
Third lecture of the week. (Friday for both sections) Instructors will have office hours, but the time should be used by you to watch the video lectures and catch on work.

A detailed schedule is given below. It is suggested that you also do the following practice problems. Most of the answers are in the back of the book, and worked out solutions are in the student manual. It is recommend that you first attempt the questions, and then check your answers.

You can download a ZIP file of all of my lecture notes here:

Math 1B03 Lecture Notes (This is a zip file of all 36 lectures)

Week 1: September 7-11
No Tutorials, Assignments, or Labs Both sections start on Wednesday, September 9, 2020
Lecture	Topic	Videos	Practice
Lecture 0	Introduction Videos WATCH FIRST	Lecture 0
Lecture 1	Introduction 1.1 Systems of Linear Equations	Lecture 1	Section 1.1: 1, 2, 7, 13, 19, 23, 27-34 [5th Ed]: 1, 2, 7, 13, 15, 19, 23, 24
Lecture 2	1.2 Row Reduction and Echelon Forms	Lecture 2	Section 1.2: 1, 3, 4, 7, 11, 13, 25-34 [5th Ed]: 1, 3, 4, 7, 11, 13, 21, 22
Week 2: September 14-18
QUIZ #1: Wednesday during class ASSIGNMENT #1: Due at 11:59PM on Sunday Sept. 20
Lecture 3	1.2 Row Reduction and Echelon Forms (Continued) Introduction to Octave	Lecture 3
Lecture 4	1.3 Vector Equations	Lecture 4	Section 1.3: 5, 7, 13, 14, 21, 23-32, 34 [5th Ed]: 5, 7, 13, 14, 21, 23, 24, 26
Lecture 5	1.4 The Matrix Equation Ax=b	Lecture 5	Section 1.4: 1, 9, 11, 13, 23-34, 35 [5th Ed]: 1, 9, 11, 13, 23-24, 26
Week 3: September 21-25
QUIZ #2: Wednesday during class LAB #1: Due at 11:59PM on Sunday Sept. 27
Lecture 6	1.5 Solution Sets of Linear Equations	Lecture 6	Section 1.5: 5, 11, 17, 23, 27-36, 47 [5th Ed]: 5, 11, 17, 19, 23-24, 35
Lecture 7	1.7 Linear Independence	Lecture 7	Section 1.7: 3, 5, 9, 15, 17, 19, 21-28, 35 [5th Ed]: 3, 5, 9, 15, 17, 19, 21, 22, 29
Lecture 8	1.8 Introduction to Linear Transformations	Lecture 8	Section 1.8: 1, 3, 5, 9, 17, 21-30, 39 [5th Ed]: 1, 3, 5, 9, 17, 21, 22, 31
Week 4: September 28-October 2
QUIZ #3: Wednesday during class ASSIGNMENT #2: Due at 11:59PM on Sunday October 4
Lecture 9	1.9 The Matrix of a Linear Transformation	Lecture 9	Section 1.9: 1, 3, 5, 7, 9, 13, 15, 17. 19, 23-32 [5th Ed]: 1, 3, 5, 7, 9, 13, 15, 17, 19, 23, 24
Lecture 10	1.6 Applications of Linear Systems	Lecture 10	Section 1.6: 1, 3, 13 [5th Ed]: 1, 3, 13
Lecture 11	2.1 Matrix Operations	Lecture 11	Section 2.1: 1, 3, 7, 9, 11, 15-24, 31 [5th Ed]: 1, 3, 7, 9, 11, 15, 16, 23
Week 5: October 5-9
QUIZ #4: Wednesday during class LAB #2: Due at 11:59PM on Sunday Oct. 11
Lecture 12	2.2 The Inverse of a Matrix	Lecture 12	Section 2.2: 3, 9, 11-20, 25, 29, 41 [5th Ed]: 3, 7, 9, 10, 15, 19, 31
Lecture 13	2.2 The Inverse of a Matrix (Continued) 2.3 Characterizations of Invertible Matrices	Lecture 13	Section 2.3: 1, 3, 5, 7, 9, 11-20, 23, 25 [5th Ed]: 1, 3, 5, 7, 9, 11, 12, 15, 25
Lecture 14	2.3 Characterizations of Invertible Matrics (Continued) 2.4 Partioned Matrices	Lecture 14	Section 2.4: 1, 3, 11-14, 17 [5th Ed]: 1, 3, 11, 12, 15
Week 6: October 12-16
FALL BREAK - no classes
Week 7: October 19-23
QUIZ #5: Wednesday during class ASSIGNMENT #3: Due at 11:59PM on Sunday Oct. 25
Lecture 15	2.7 Applications to Computer Graphics	Lecture 15	Section 2.7: 1, 3, 7, 14 [5th Ed]: 1, 3, 7, 14
Lecture 16	3.1 Introduction to Determinants	Lecture 16	Section 3.1: 1, 3, 5, 7, 9, 11, 15, 25, 39-42 [5th Ed]: 1, 3, 5, 7, 9, 11, 15, 25, 39, 40
Lecture 17	3.2 Properties of Determinants	Lecture 17	Section 3.2: 3, 7, 11, 15, 17, 27-34, 37, 45 [5th Ed]: 3, 7, 11, 15, 17, 27, 28, 31, 39
Week 8: October 26-30
QUIZ #6: Wednesday during class LAB #3: Due at 11:59PM on Sunday, November 1
Lecture 18	3.3 Cramer's Rule, Volume, and Linear Transformations	Lecture 18	Section 3.3: 1, 3, 5, 11, 19, 25 [5th Ed]: 1, 3, 5, 11, 19, 25
Lecture 19	4.1 Vector Spaces and Subspaces	Lecture 19	Section 4.1: 1, 3, 5, 7, 11, 13, 21, 23-32 [5th Ed]: 1, 3, 5, 7, 11, 13, 21, 23, 24
Lecture 20	4.1 Vector Spaces and Subspaces (continued) 4.2 Null Spaces, Column Spaces, and Linear Transformations	Lecture 20	Section 4.2: 3, 5, 7, 13, 17, 25-38, 43 [5th Ed]: 3, 5, 7, 13, 17, 25, 26, 31
Week 9: November 2-6
QUIZ #7: Wednesday during class ASSIGNMENT #4: Due at 11:59PM on Sunday Nov. 8
Lecture 21	4.2 Null Spaces, Column Spaces, and Linear Transformations (Continued)	Lecture 21
Lecture 22	4.3 Linear Independent Sets; Bases	Lecture 22	Section 4.3: 3, 5, 7, 11, 13, 15, 21-32, 34 [5th Ed]: 3, 5, 7, 11, 13, 15, 21, 22, 34
Lecture 23	4.4 Coordinate Systems	Lecture 23	Section 4.4: 3, 5, 7, 11, 13, 15-20, 21, 25 [5th Ed]: 3, 5, 7, 11, 13, 15, 16, 17, 21
Week 10: November 9-13
QUIZ #8: Wednesday during class LAB #4: Due at 11:59PM on Sunday, November 15
Lecture 24	6.1 Inner Product, Length, and Orthgonality 6.2 Orthogonal Sets	Lecture 24	Section 6.1: 1, 5, 7, 19-28, 35 [5th Ed]: 1, 5, 7, 19, 20, 27 Section 6.2: 3, 5, 9, 21, 23-32 [5th Ed]: 3, 5, 9, 21, 23, 24
Lecture 25	6.3 Orthogona Projections 6.4 Gram-Schmidt	Lecture 25	Section 6.3: 3, 5 [5th Ed]: 3, 5 Section 6.4: 1, 3, 5, 7, 9 [5th Ed]: 1, 3, 5, 7, 9
Lecture 26	4.5 The Dimension of a Vector Space	Lecture 26	Section 4.5: 3, 5, 11, 13, 15, 17-26, 31 [5th Ed]: 3, 5, 11, 13, 15, 19, 20, 25
Week 11: November 16-20
QUIZ #9: Wednesday during class ASSIGNMENT #5: Due at 11:59PM on Sunday Nov. 22
Lecture 27	4.5 The Dimension of a Vector Space II (4.6 in 5th Edition)	Lecture 27	Section 4.5: 11, 13, 15, 35, 43-48 [Section 4.6 5th Ed]: 1, 3, 5, 7, 17, 18
Lecture 28	5.1 Eigenvalues and Eigenvectors	Lecture 28	Section 5.1: 1, 5, 7, 11, 13, 19, 21-30, 33 [5th Ed]: 1, 5, 7, 11, 13, 19, 21, 22, 25
Lecture 29	5.2 Characteristic Equation	Lecture 29	Section 5.2: 3, 7, 9, 13, 17, 19, 21-30 [5th Ed]: 3, 7, 9, 13, 17, 19, 21, 22
Week 12: November 23-27
QUIZ #10: Wednesday during class LAB #5: Due at 11:59PM on Friday November 29
Lecture 30	5.3 Diagonalization	Lecture 30	Section 5.3: 1, 5, 7, 9, 11, 21-28, 31 [5th Ed]: 1, 5, 7, 11, 21, 22, 25
Lecture 31	5.3 Diagonalization (Continued)	Lecture 31
Lecture 32	5.4 Eigenvectors and Linear Transformations	Lecture 32	Section 5.4: 1, 3, 5, 9, 11, 15, 17-20, 21 [5th Ed]: 1, 7, 8, 13, 15, 19
Week 13: November 30-December 4
QUIZ #11: Wednesday during class No assignments or labs this week
Lecture 33	Appendix B Complex Numbers	Lecture 33
Lecture 34	5.5 Complex Eigenvalues	Lecture 34	Section 5.5: 1, 3, 5, 13, 15, 23-26 [5th Ed]: 1, 3, 5, 13, 15
Lecture 35	5.6 Discrete Dynamical Systems	Lecture 35	Section 5.6: 1, 5, 7ac, 9, 11, 13 [5th Ed]: 1, 5, 7ac, 9, 11, 13
Week 14: December 7-9
ASSIGNMENT #6: Due at 11:59PM on Wednesday, Dec. 9 (NOTE CHANGE!!!)
Lecture 36	5.9 Applications to Markov Chains (4.9 in 5th Edition)	Lecture 36	Section 5.9: 3, 5, 7, 13, 15, 17, 19 [Section 4.9 5th Ed]: 3, 5, 7, 13
Lecture 37	Review

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McMaster Polices

1. McMaster University Statement on Inclusivity and Academic Integrity. The University values integrity, inclusiveness and teamwork, and strives to support the personal and collective growth of the McMaster student community.

These values are foundational to ensuring campus environments -- both in-person and virtual -- are conducive to personal wellbeing and academic success.

2. Inclusivity and a Culture of Respect. As a McMaster student, you have the right to experience and the responsibility to demonstrate respectful and dignified interactions within all of our living, learning and working communities. Expectations are described in Code of Student Rights and Responsibilities

It is essential that students be mindful of their interactions online, as the Code remains in effect in virtual learning environments. The Code applies to any interactions that adversely affect, disrupt, or interfere with reasonable participation in University activities. Student disruptions or behaviours that interfere with university functions on online platforms (e.g. use of Avenue 2 Learn, WebEx or Zoom for delivery), will be taken very seriously and will be investigated. Outcomes may include restriction or removal of the involved students' access to these platforms. Additional information about the Code and netiquette can be found here.

3. Academic Integrity and Honesty. As a McMaster student, you are expected to exhibit honesty and ethical behaviour in all aspects of the learning process. The academic credentials that you earn are rooted in the principles of honesty and academic integrity.

Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: Grade of F assigned for academic dishonesty), and/or suspension or expulsion from the university.

It is your responsibility to understand what constitutes academic dishonesty. For information on the various types of academic dishonesty please refer to the Academic Integrity Policy, located at: http://www.mcmaster.ca/academicintegrity/

The following illustrates only three forms of academic dishonesty:

plagiarism, e.g. the submission of work that is not one's own or for which other credit has been obtained.
improper collaboration in group work,
copying or using unauthorized aids in tests and examinations.

Some helpful information can be found here.

4. Academic Accommodation of Students with Disabilities. Students with disabilities who require academic accommodation must contact Student Accessibility Services (SAS) to make arrangements with a Program Coordinator. Student Accessibility Services can be contacted by phone 905-525-9140 ext. 28652 or e-mail sas@mcmaster.ca. For further information, consult McMaster University's Academic Accommodation of Students with Disabilities policy.

5. Requests for Relief for Missed Academic Term Work. If you have missed work, it is your responsibility to take action. If you are absent from the university for medical and non-medical (personal) situations, lasting fewer than 3 days, you may report your absence, once per term, without documentation, using the McMaster Student Absence Form (MSAF). See Requests for Relief for Missed Academic Term Work

Absences for a longer duration or for other reasons must be reported to your Faculty/Program office, with documentation, and relief from term work may not necessarily be granted. In Math 1B03, the percentages of the missed work will be transferred to the final examination. Please note that the MSAF may not be used for term work worth 25% or more, nor can it be used for the final examination.

6. Academic Accommodation for Religious, Indigenous or Spiritual Observances (RISO). Students requiring academic accommodation based on religious, indigenous or spiritual observances should follow the procedures set out in the RISO policy. Students requiring a RISO accommodation should submit their request to their Faculty Office normally within 10 working days of the beginning of term in which they anticipate a need for accommodation or to the Registrar's Office prior to their examinations. Students should also contact their instructors as soon as possible to make alternative arrangements for classes, assignments, and tests.

7. Important Message. The instructor and university reserve the right to modify elements of the course during the term. The University reserves the right to change the dates and deadlines for any or all courses in extreme circumstances (e.g., severe weather, labour disruptions, etc.). Changes will be communicated through regular McMaster communication channels, such as McMaster Daily News, A2L and/or McMaster email. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.

8. On-line Statement for Courses Requiring Online Access or Work. In this course we will be using Zoom or Teams, Avenue-to-Learn, Crowdmark, Octave-Online, and https://www.childsmath.ca/childsa/forms/main_login.php, a local website hosted by the department. Students should be aware that, when they access the electronic components of this course, private information such as first and last names, user names for the McMaster e-mail accounts, and program affiliation may become apparent to all other students in the same course. The available information is dependent on the technology used. Continuation in this course will be deemed consent to this disclosure. If you have any questions or concerns about such disclosure please discuss this with the course instructor.

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Math 1B03 - Linear Algebra I
(Fall 2020)

News

Schedule

Homework/Quizzes

Handouts

Grading Scheme

Policies

Course Information

News (Last Updated: August 31)

Schedule

Homework, Labs, and Quizzes

Handouts

Grading Scheme

McMaster Polices

Math 1B03 - Linear Algebra I (Fall 2020)

News

Schedule

Homework/Quizzes

Handouts

Grading Scheme

Policies

Course Information

News (Last Updated: August 31)

Schedule

Homework, Labs, and Quizzes

Handouts

Grading Scheme

McMaster Polices

Math 1B03 - Linear Algebra I
(Fall 2020)