Assignments:
There will be 6
assignments this semester. Your lowest assignment score will be
droped when computing your assignment
average in the course. Assignments are worth 10% of your final grade
in this course, so each assignment will be worth 2% of your final
grade (not counting your lowest assignment grade). Assignments
are conducted online through childsmath.
You can access them by clicking on the following link and
following the posted instructions: https://www.childsmath.ca/childsa/forms/main_login.php
The assignment due dates (tentative) are as follows:
There
will be three 50minute tests held in person on October 6, November 3,
and November 24 (tentative dates) during the scheduled class time.
Further details on the tests will be given in class and announced on
the course web page. The McMaster standard calculator is allowed on
all tests.
A final
exam for this courses will be scheduled by
the registrar. Details will be posted on the course website as
they become available.
Lecture Schedule (tentative):
Lecture schedule for Math 2LA3 (tentative)
The following lecture
schedule is tentative and could change as the term proceeds. The
chapter and section information are relative to the 6th edition of
Linear Algebra and Its Applications by Lay, Lay and McDonald.
A more detailed, lecture by lecture schedule can be found below this
list.
Week 1, September 69
Review from Math 1B3
(Chapters 1, 2, and 4)
Practice Problems: Section 2.8
#11, 13, 18, 19, 20, 31, 33, 45 (use WolframAlpha
or some other software); section 2.9, #9, 13.
Week 2, September 1216
Continuation of
Review.
Practice problems: 4.1, #11, 13,
43 (don't do this by hand); 4.2 #5, 49 (use technology); 4.3 #15, 17;
4.4, #3, 7, 39 (not by hand); 4.5, #9, 11, 13, 53 (use tech)
Week 3, September 1923
Introduction to
linear programming (Chapter 9, sections 2, 3), Optimization problems.
Practice problems: Section 9.2: #1, 3, 5, use desmos to solve 7, 9, 15, 16, 17
Week
4, September 2630
Optimization problems
continued (Section 9.3)
Practice problems: Section 9.3: #1, 3, 5, 13, 15,
16 (do some of these by hand, and some using Wolfram Alpha,
Matlab, or some other software)
Week 5, October 37 (test 1, October 6, in class)
Review of eigenvalues
and eigenvectors; Chapter 5 sections 1  3
Practice problems: Section 5.1, #13, 15, 45, 47 (for 45, 47  use WolframAlpha or equivalent), 5.2: 9, 11, 35 , 5.3: 17, 19, 41 (with any available tech)
Week
6, October 1014
Reading
week,
no classes
Week 7, October 1721
Review, continued, orthogonality; Chapter 6, sections 1 3
Week 8, October 2428
GramSchmidt, QR decomposition,
projection matrices, Leastsquares; Chapter 6, sections 4, 5
Practice problems: Section 6.1: 118; Section
6.2: 110, 13, 15, 21, 22; Section 6.3: 1, 5, 9, 17; Section 6.4: 1,
3, 5, 9, 11 13, 15
Week 9, October 31November 4 (test 2, November 3, in class)
Leastsquares,
Orthogonal diagonalization;
Chapter 6, sections 5, 6, Chapter 7, section 7.1
Practice problems: Section 6.5: 2  6, 911, 15 Section 7.1: 1322
Added: Section 6.6:14, Section 7.1: 39, 40
Week
10, November 711
The spectral theorem,
quadratic forms. Chapter 7, sections 1 and 2
Practice problems: Section 7.2: 920
Week 11, November 1418
Constrained
Optimization Singular value decomposition (SVD); Chapter 7, sections 3
and 4
Section 7.4: 116, 2629 (use Wolfram Alpha or other software).
Added: Section 7.3:1, 3 (a), (b), 7, 9, 11
Week 12, November 2125 (test #3,
November 24, in class)
SVD
Week 13, November 28December 2
SVD, Principal component
analysis
Practice problems: Section 7.5: 1, 2, 7
Week 14, December 58
SVD applications, course wrapup
Lecture # 
Date 
topics covered 
reading/resources/comments 
1 
7/09/22 
course introduction, the vector space R^n 
Invertible
Matrix Theorem Lecture #1 notes Introduction, Section 1.3 
2 
8/09/22 
matrices, matrix multiplication, subspaces of R^n 
Sections 1.3, 1.7, 2.1, 2.8 of the textbook 
3 
12/09/22 
bases, rank, reduced row echelon form 
Sections 1.2, 2.8, 2.9 
4 
14/09/22 
Basis for a null space. 
Sections 2.3, 2.8, 2.9, 4.2, 4.3, 4.4, 4.5 
5 
15/09/22 
invertible matrices, introduction to linear programming 
Sections 3.2, 4.5, 9.2 
6 
19/09/22 

Section 9.2 
7 
21/09/22 

Sections 9.2, 9.3 
8 
22/09/22 
continued 
Sections 9.2, 9.3 
9 
26/09/22  the simplex method  Section 9.3 Lecture #9 notes Simplex Method Example from the lecture 
10 
28/09/22  continued  Section 9.3 Lecture #10 notes 
11 
29/09/22  continued, review of eigenvalues, eigenvectors  Sections 9.3, 5.1, 5.2 Lecture #11 notes 
12 
3/10/22  review of eigenvalues, eigenvectors  Sections 5.1, 5.2 Lecture #12 notes 
13 
5/10/22  similarity and diagonalizability 
Sections 5.2, 5.3 Lecture #13 notes 
14 
6/10/22  midterm test #1  
15 
17/10/22  continued, diagonalization  Sections 5.1, 5.2, 5.3 Lecture #15 notes 
16 
19/10/22  orthogonality, orthogonal complement  Sections 6.1, 6.2 Lecture #16 notes 
17 
20/10/22  orthogonal and orthonormal bases, orthogonal projections  Sections 6.2, 6.3 Lecture #17 notes 
18 
24/10/22  orthogonal projections, GramSchmidt Process  Sections 6.3, 6.4 Lecture #18 notes 
19 
26/10/22  GramSchmidt Process, QR decomposition  Section 6.4 Lecture #19 notes 
20 
27/10/22  QR factorization, projection matrices  Sections 6.4, 6.5 Lecture #20 notes 
21 
31/10/22  leastsquares  Section 6.5 Lecture #21 notes 
22 
2/11/22  leastsquares  Section 6.5 Lecture #22 notes 
23 
3/11/22  midterm test #2  
24 
7/11/22  symmetric matrices  Section 7.1 Lecture #24 notes 
25 
9/11/22  symmetric matrices  Section 7.1 Lecture #25 notes 
26 
10/11/22  quadratic forms  Section 7.2 Lecture #26 notes 
27 
14/11/22  quadratic forms  Sections 7.2, 7.3 Lecture #27 notes 
28 
16/11/22  constrained optimization  Section 7.3 Lecture #28 notes 
29 
17/11/22  SVD  Section 7.4 Lecture #29 notes 
30 
21/11/22  SVD  Section 7.4 Lecture #30 notes 
31 
23/11/22  SVD  Section 7.4 Lecture #31 notes 
32 
24/11/22  midterm test #3  
33 
28/11/22  SVD  Section 7.4 Lecture #33 notes 
34 
30/11/22  Principal Component Analysis  Section 7.5 Lecture #34 notes 
35 
1/12/22  Principal Component Analysis  Section
7.5 Lecture #35 notes 
36 
5/12/22  image compression  Image compression demo Lecture #36 notes 
37  7/12/22  facial recognition  Eigenfaces
example Faces DataSet Face recognition Eigenfaces Lecture #37 notes 
38  8/12/22  course wrap up, review  Lecture #38 notes 