Department of Mathematics, College of Staten Island, City University of New York (CUNY)

Linear Algebra: MATH 338, Section 19357 - Fall 2020 Course Outline

Monday & Wednesday, 2:30 pm - 4:25 pm

Prof. Ilya Kofman


Textbook:  Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, 2016. ISBN: 978-09802327-7-6. You can rent or buy, new or used, from any store.

Videos:  You are expected to view each video listed below before class, so that we can discuss the material further in class.

Homework:  Webwork problems must be submitted online. To pass this course, the Webwork problems are the minimum requirement; to earn an excellent grade, you will have to do the other assigned problems in your textbook. Answers to exercises in the textbook are at I highly recommend working jointly on homework problems with fellow students, but in the end you must hand in your own work.

Webwork:  Webwork is a free online system that provides individualized homework problems, gives immediate feedback, and allows you to correct mistakes until the due date. Later, you can see solutions online. Webwork is required in this course, and it is a major part of your grade. Webwork website

MATLAB:  MATLAB is powerful computer algebra software designed to solve linear algebra problems. Our textbook has a lot of MATLAB material, and learning to use MATLAB will help you in this course. You can access MATLAB online using CUNY Virtual Desktop.

Grading:  The course grade will be determined (subject to changes announced in class) by your online participation and your scores on Webwork, homework, exams and final exam. Without exception, you must pass the exams to pass this course, and you must take the final exam at the time scheduled by the college.

Help:  My office hours are Mondays and Wednesdays, 4:30pm-5:45pm. Email is the fastest way to contact me.

How to Study:  (1) Watch the appropriate video before class. (2) Attend class (attendance is mandatory).  (3) Read the relevant sections after class.  (4) Do the homework. Leave time to think about it!  (5) Use the Blackboard discussion board or visit me during office hours with any remaining questions.  (6) To study for a math exam, you must DO MORE PROBLEMS from past exams, homework and textbook.

Class Topic Videos Read Exercises Webwork
Aug 26 Vectors and Linear Combinations, Lengths and Dot Products 3B1B-E1 and 3B1B-E2 and
KA-dot product
§1.1, 1.2 1.1: p.8: 2,4,6,9,10,17,26
1.2: p.18: 1,3,4,6,8,9,12,19,21,29
Set 1
Aug 31 Matrices, Vectors and Linear Equations Strang 1 §1.3, 2.1 1.3: p. 29: 1,2,4,5,7
2.1: p. 41: 4,5,6,7,9,10,13,18,27
Set 2
Sep 2 Elimination Strang 2 and another example §2.2, 2.3 2.2: p. 53: 1,2,4,5,11,12,13
2.3: p. 66: 1,3,4,8,11,14,18,25,27,28
Set 3
Sep 9 Matrix Operations, Inverse Matrices Strang 3 §2.4, 2.5 2.4: p. 77: 1,3,5,7,13,14,15,17,19,27
2.5: p. 92: 1,4,6,7,8,11,15,16,21,22,24,27
Sets 4,5
Sep 14 Review        
Sep 16 EXAM 1
Factorization A=LU
p. 104: 1,2,3,4,6,9,12,15,
MATLAB examples for which you must import the function slu.m
Sep 21 Factorization A=LU
Transposes and Permutations
Strang 4
Strang 5
p.117: 2,4,8,16,17,20,22*
Set 6
Sep 23 Spaces of Vectors Strang 6 §3.1 p. 131: 1,3,5,9,11,15,19,20,23,25 Set 7
Sep 29 Nullspace of A Strang 7 §3.2 p. 142: 1,2,3,5,8,9,11,13,14,16,24,29 Set 8
Sep 30 Complete Solution to Ax=b Strang 8 §3.3 p. 158: 1,2,4,6,8,12,13,14,16,18,25 Set 9
Oct 5 Review        
Oct 7 EXAM 2
Independence, Basis and Dimension
Oct 14 Independence, Basis and Dimension Strang 9 §3.4 p. 175: 1,2,3,6,8,9,11,12,15,18,20,25 Sets 10,11,12
Oct 19 Dimensions of the Four Subspaces Strang 10 §3.5 p. 190: 1,2,4,6,9,11,12,16,24 Set 13
Oct 21 Orthogonality of the Four Subspaces Strang 14 §4.1 p. 202: 1,3,5,6,8,9,10,11,12,16,28 Set 14
Oct 26 Projections and Least Squares Approximations Strang 15 and Strang 16 §4.2, 4.3 4.2: p. 214: 1,3,8,9,11,13,17,21,24,29
4.3: p. 229: 1,2,3,4,5,8,12
Sets 15,16
Oct 28 Review        
Nov 2 EXAM 3
Orthogonal Bases and Gram-Schmidt
Nov 4 Orthogonal Bases and Gram-Schmidt Strang 17 §4.4 p. 242: 1,2,4,5,21 Set 17
Nov 9 Determinants Strang 18 and Strang 19 §5.1, 5.2 5.1: p.254: 1,3,8,9,10,11,14,23,24,27,28
5.2: p.266: 1,2,3,4,5
Set 18
Nov 11 Cramer's Rule, Inverses, and Volumes
Strang 20 and 3B1B-E12 §5.3 p. 283: 2,3,16,17 Set 19
Nov 16 Eigenvalues Strang 21 and 3B1B-E14 §6.1 p. 298: 1,3,5,6,8,16,17,21,23,27. See Explained Visually Set 20
Nov 18 Diagonalizing a Matrix Strang 22 §6.2 p.314: 1,3,4,6,11,12,13,14,15,21,26 Set 21
Nov 23 Review        
Nov 30 EXAM 4
Linear Transformations
Dec 2 Linear Transformations 3B1B-E3 and 3B1B-E4 and 3B1B-E5 §8.1 p.407: 1,3,6,10,12 Set 22
Dec 7 Matrix of a Linear Transformation Strang 30 §8.2 p.418: 5,6,7,10,11,14,15,16. See applet Set 23
Dec 9 Review Strang 34      

Online resources: 

MIT OpenCourseWare Linear Algebra  Complete online linear algebra course.

Khan Academy Linear Algebra  Complete online linear algebra course.

3Blue1Brown Essence of Linear Algebra  Excellent online videos.

Mathmatize  Linear algebra problems in an online app

Eigenvectors and Eigenvalues Explained Visually linear transformations applet

How Google Finds Your Needle in the Web's Haystack

Attendance policy: Attendance is mandatory. Unauthorized absences from four or more classes will result in a course grade of WU (Withdrew Unofficially).

Disability policy: Qualified students with disabilities will be provided reasonable academic accommodations if determined eligible by the Office for Disability Services. Prior to granting disability accommodations in this course, the instructor must receive written verification of student's eligibility from the Office of Disability Services, which is located in 1P-101. It is the student's responsibility to initiate contact with the Office for Disability Services staff and to follow the established procedures for having the accommodation notice sent to the instructor.

Integrity policy: CUNY's Academic Integrity Policy is available online at

Important Dates: