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

Linear Algebra: MATH 338 - Fall 2019 Course Outline

Monday & Wednesday, 2:30 pm - 4:25 pm in Room 3S-104

Prof. Ilya Kofman

Office:   1S-209   phone: (718) 982-3615

Textbook:  Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, 2016. ISBN: 978-09802327-7-6.

Homework:  Answers to many exercises are in the back of the book. 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. 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. The CSI math department computer labs have MATLAB, or you can access MATLAB online using CUNY Virtual Desktop.

Grading:  The course grade will be determined (subject to changes announced in class) by 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 1pm-2:15pm in my office, 1S-209. Email is the fastest way to contact me. Also, free math tutoring is available.

How to Study:  (1.) Come to class (attendance is mandatory).  (2.) Read the relevant sections after class.  (3.) Do the homework. Leave time to think about it!  (4.) Come to my office hours or the help room with any remaining questions.  (5.) To study for a math exam, you must DO MORE PROBLEMS from past exams, homework and textbook.

Class Topic Read Exercises
Aug 28 Vectors and Linear Combinations, Lengths and Dot Products §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
Sep 4 Matrices, Vectors and Linear Equations §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
Sep 5 Elimination §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
Sep 9 Matrix Operations, Inverse Matrices §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
Sep 11 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 18 Factorization A=LU
Transposes and Permutations
p.117: 2,4,8,16,17,20,22*
Sep 23 Spaces of Vectors §3.1 p. 131: 1,3,5,9,11,15,19,20,23,25
Sep 25 Nullspace of A §3.2 p. 142: 1,2,3,5,8,9,11,13,14,16,24,29
Oct 2 Review    
Oct 7 EXAM 2
Complete Solution to Ax=b
Oct 16 Complete Solution to Ax=b §3.3 p. 158: 1,2,4,6,8,12,13,14,16,18,25
Oct 21 Independence, Basis and Dimension §3.4 p. 175: 1,2,3,6,8,9,11,12,15,18,20,25
Oct 23 Dimensions of the Four Subspaces §3.5 p. 190: 1,2,4,6,9,11,12,16,24
Oct 28 Orthogonality of the Four Subspaces §4.1 p. 202: 1,3,5,6,8,9,10,11,12,16,28
Oct 30 Review    
Nov 4 EXAM 3
Nov 6 Projections and Least Squares Approximations §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
Nov 11 Orthogonal Bases and Gram-Schmidt §4.4 p. 242: 1,2,4,5,21
Nov 13 Determinants §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
Nov 18 Cramer's Rule, Inverses, and Volumes
§5.3 p. 283: 2,3,16,17
Nov 20 Eigenvalues §6.1 p. 298: 1,3,5,6,8,16,17,21,23,27. See Explained Visually
Nov 25 Review    
Nov 27 EXAM 4
Diagonalizing a Matrix
Dec 2 Diagonalizing a Matrix §6.2 p.314: 1,3,4,6,11,12,13,14,15,21,26
Dec 4 Linear Transformations §8.1 p.407: 1,3,6,10,12
Dec 9 Matrix of a Linear Transformation §8.2 p.418: 5,6,7,10,11,14,15,16. See applet
Dec 11 Review   Sample problems for chapters 6,8

Online resources: 

MIT Linear Algebra  MIT Videos, Problem Sets and Exams

MIT OpenCourseWare Linear Algebra  Complete online linear algebra course.

Khan Academy Linear Algebra  Complete online linear algebra course.

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: