Math 18: Linear Algebra

Lectures A (Eggers) & B & C (Kemp)


Course Information

Instructional Staff

John Eggers Instructor APM 5802
Todd Kemp Instructor APM 5202
Prashant Singh Teaching Assistant MAYER 5722
Yiwei Sang Teaching Assistant
Marc Loschen Teaching Assistant APM 6446
Ashwin Nayak Teaching Assistant APM 2313
Rose Elliott Smith Teaching Assistant
Eric Lybrand Teaching Assistant APM 6444
Anirudh Ravichandran Teaching Assistant APM 5768
Xinyi Luo Teaching Assistant

We will be communicating with you and making announcements through an online question and answer platform called Piazza (sign up link: We ask that when you have a question about the class that might be relevant to other students, you post your question on Piazza instead of emailing us. That way, everyone can benefit from the response. Posts about homework or exams on Piazza should be content based. While you are encouraged to crowdsource and discuss coursework through Piazza, please do not post complete solutions to homework problems there. Questions about grades should be brought to the instructors, in office hours. You can also post private messages to instructors on Piazza, which we prefer over email.

Our office hours can be found in the following calendar.

Calendar of Meeting Times

Class Meetings

Lecture A00 (Eggers) Monday, Wednesday, Friday8:00am - 8:50amLEDDN AUD
Lecture B00 (Kemp) Monday, Wednesday, Friday10:00am - 10:50amCENTR 119
Lecture C00 (Kemp) Monday, Wednesday, Friday12:00pm - 12:50pmCENTR 119
Discussion A01 (Singh) Thursday8:00am - 8:50amAPM 2301
Discussion A02 (Singh) Thursday9:00am - 9:50amAPM 2301
Discussion A03 (Sang) Thursday10:00am - 10:50amAPM 2301
Discussion A04 (Sang) Thursday11:00am - 11:50amAPM 2301
Discussion A05 (Loschen) Thursday12:00pm - 12:50pmAPM 2301
Discussion A06 (Loschen) Thursday1:00pm - 1:50pmAPM 2301
Discussion B01 (Nayak) Thursday8:00pm - 8:50amWLH 2208
Discussion B02 (Nayak) Thursday9:00am - 9:50amWLH 2208
Discussion B03 (Elliott Smith) Thursday10:00am - 10:50amWLH 2208
Discussion B04 (Elliott Smith) Thursday11:00am - 11:50amWLH 2208
Discussion B05 (Lybrand) Thursday12:00pm - 12:50pmWLH 2208
Discussion B06 (Lybrand) Thursday1:00pm - 1:50pmWLH 2208
Discussion C01 (Ravichandran) Thursday2:00pm - 2:50pmAPM 2301
Discussion C02 (Ravichandran) Thursday3:00pm - 3:50pmAPM 2301
Discussion C03 (Luo) Thursday4:00pm - 4:50pmAPM 2301
Discussion C04 (Luo) Thursday5:00pm - 5:50pmAPM 2301
Discussion C05 (Ravichandran) Thursday6:00pm - 6:50pmAPM 2301
Discussion C06 (Ravichandran) Thursday7:00pm - 7:50pmAPM 2301
First Midterm Exam Wednesday, Jan 318:00pm - 10:00pmGH 242 & YORK 2622 & YORK 2722
Second Midterm Exam Wednesday, Feb 288:00pm - 10:00pmGH 242 & PETER 108 & PETER 110
Final Exam Saturday, Mar 1711:30am - 2:30pmGH 242 & PETER 108 & YORK 2722



Course:  Math 18

Title:  Linear Algebra

Credit Hours:  4  (Students may not receive credit for both Math 18 and 31AH.)

Prerequisite:  Math Placement Exam qualifying score, or AP Calculus AB score of 2, or SAT II Math Level 2 score of 600 or higher, or Math 3C, or Math 4C, or Math 10A, or Math 20A, or consent of instructor.

Catalog Description:  Matrix algebra, Gaussian elimination, determinants, Linear and affine subspaces, bases of Euclidean spaces. Eigenvalues and eigenvectors, quadratic forms, orthogonal matrices, diagonalization of symmetric matrices. Applications. Computing symbolic and graphical solutions using Matlab. See the UC San Diego Course Catalog.

Textbook: Linear Algebra and its Applications, by David C. Lay, Steven R. Lay, and Judi J. McDonald; published by Pearson (Addison Wesley).

Subject Material:  We will cover parts of chapters 1-7 of the text.

Lecture:  Attending the lecture is a fundamental part of the course; you are responsible for material presented in the lecture whether or not it is discussed in the textbook.  You should expect questions on the exams that will test your understanding of concepts discussed in the lecture.

Reading:  Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment; you are responsible for material in the assigned reading whether or not it is discussed in the lecture.

Calendar of Lecture Topics:   The following calendar is subject to revision during the term. The section references are only a guide; our pace may vary from it somewhat.

Week Monday Tuesday Wednesday Thursday Friday Saturday
Jan 8
1.1 Systems of linear equations
Jan 9 Jan 10
1.2 Row reduction & echelon forms
Jan 11
Jan 12
1.3 Vector equations
Jan 13
Jan 15
Martin Luther
King Day
Jan 16 Jan 17
1.4 Matrix equation
Ax = b
Jan 18
Jan 19
1.5 Solution sets
Jan 20
Jan 22
1.7 Linear independence
Jan 23 Jan 24
1.8 Linear transformations
Jan 25
Jan 26
1.9 The matrix of a linear transformation
Jan 27
Jan 29
2.1 Matrix operations
Jan 30 Jan 31
Catch up & Review
Feb 1
Feb 2
2.2, 2.3 Inverse of a matrix
Last Day to
Drop w/o 'W'
Feb 3
Feb 5
4.1 Vector spaces and subspaces
Feb 6 Feb 7
4.2 Null spaces & column spaces
Feb 8
Feb 9
4.3 Linear independent sets; bases
Feb 10
Feb 12
4.5 Dimension
Feb 13 Feb 14
4.6 Rank
4.4 Coordinate systems
Feb 15
Feb 16
3.1 Determinants
3.2 Properties of determinants
Feb 17
Feb 19
Presidents Day
Feb 20 Feb 21
3.3 Determinants and volume
Feb 22
Feb 23
5.1 Eigenvectors and eigenvalues
Feb 24
Feb 26
5.2 Characteristic polynomial
Feb 27 Feb 28
Catch up & Review
Mar 1
Mar 2
5.3 Diagonalization
Mar 3
Mar 5
6.1, 6.7 Inner product,
length, & orthogonality
Mar 6 Mar 7
6.2 Orthogonal sets
Mar 8
Mar 9
6.3 Orthogonal projections
Last Day to
Drop w/o 'F'
Mar 10
10 Mar 11
6.4 Gram-Schmidt orthogonalization
Mar 13 Mar 14
7.1 Spectral Theorem
Mar 15
Mar 16
Mar 17

Homework:  Homework is a very important part of the course and in order to fully master the topics it is essential that you work carefully on every assignment and try your best to complete every problem. We will have two different kinds of homework assignments in this class: online homework (which will be graded) and "paper-and-pen" homework (which will not be graded).

MATLAB:   In applications of linear algebra, the theoretical concepts that you will learn in lecture are used together with computers to solve large scale problems.  Thus, in addition to your written homework, you will be required to do homework using the computer language MATLAB.  The Math 18 MATLAB Assignments page contains all information relevant to the MATLAB component of Math 18. The first assignment is due in week 2 of the course.  You can do the homework on any campus computer that has MATLAB.  Questions regarding the MATLAB assignments should be directed to the TAs.  There are also tutors available beginning Thursday or Friday of the first week of classes in B432 of AP&M.  Please turn in your homework via Gradescope, as described on the MATLAB page, by 11:59pm on the indicated due date (as indicated on the Math 18 MATLAB Assignments page). In general, MATLAB homework will be accepted up to 48 hours after the deadline, but a 10% late penalty will be assessed if it is not uploaded before the deadline. In case you have to miss one MATLAB assignment, your lowest MATLAB homework score will be dropped.  There will be a MATLAB quiz at the end of the quarter.

Midterm Exams:  There will be two midterm exams given during the quarter.  See above for the dates and times of the midterm exams.   You may bring one 8.5 by 11 inch sheet of paper with handwritten notes (on both sides) with you to each midterm exam; no other notes (or books) will be allowed.  No calculators, phones, or other electronic devices will be allowed during the midterm exams.   There will be no makeup exams.

Final Examination:  The final examination will be held at the date and time stated above.

Administrative Links:    Here are two links regarding UC San Diego policies on exams:

Regrade Policy:  

Administrative Deadline:  Your scores for all graded work will be posted to TritonEd.

Grading: Your course grade will be determined by your cumulative average at the end of the term and will be based on the following scale:

A+ A A- B+ B B- C+ C C-
97 93 90 87 83 80 77 73 70
Your cumulative average will be the best of the following two weighted averages: In addition,  you must pass the final examination in order to pass the course.  Note: Since there are no makeup exams, if you miss a midterm exam for any reason, then your course grade will be computed with the second option. There are no exceptions; this grading scheme is intended to accommodate emergencies that require missing a midterm exam.

Academic Integrity:  UC San Diego's code of academic integrity outlines the expected academic honesty of all students and faculty, and details the consequences for academic dishonesty. The main issues are cheating and plagiarism, of course, for which we have a zero-tolerance policy. (Penalties for these offenses always include assignment of a failing grade in the course, and usually involve an administrative penalty, such as suspension or expulsion, as well.) However, academic integrity also includes things like giving credit where credit is due, and treating your peers respectfully in class. In addition, here are a few of our expectations for etiquette in and out of class.


Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD) which is located in University Center 202 behind Center Hall. Students are required to present their AFA letters to the instructor (please make arrangements to contact your instructor privately) and to the OSD Liaison in the department in advance (by the end of Week 2, if possible) so that accommodations may be arranged. For more information, see here.



Here are some additional resources for this course, and math courses in general.

Lecture Notes

Here are the notes from the lectures (for each of lectures B and C). The "skeleton" of notes from before the lecture begins will be posted the day before the lecture (in case you wish to print it or view it as the lecture proceeds), while the completed notes will be posted soon after the lecture.

1B Math18-Lecture1-B00-before.pdf Math18-Lecture1-B00-after.pdf
1C Math18-Lecture1-C00-before.pdf Math18-Lecture1-C00-after.pdf
2B Math18-Lecture2-B00-before.pdf Math18-Lecture2-B00-after.pdf
2C Math18-Lecture2-C00-before.pdf Math18-Lecture2-C00-after.pdf
3B Math18-Lecture3-B00-before.pdf Math18-Lecture3-B00-after.pdf
3C Math18-Lecture3-C00-before.pdf Math18-Lecture3-C00-after.pdf
4B Math18-Lecture4-B00-before.pdf Math18-Lecture4-B00-after.pdf
4C Math18-Lecture4-C00-before.pdf Math18-Lecture4-C00-after.pdf
5B Math18-Lecture5-B00-before.pdf Math18-Lecture5-B00-after.pdf
5C Math18-Lecture5-C00-before.pdf Math18-Lecture5-C00-after.pdf
6B Math18-Lecture6-B00-before.pdf Math18-Lecture6-B00-after.pdf
6C Math18-Lecture6-C00-before.pdf Math18-Lecture6-C00-after.pdf
7B Math18-Lecture7-B00-before.pdf Math18-Lecture7-B00-after.pdf
7C Math18-Lecture7-C00-before.pdf Math18-Lecture7-C00-after.pdf
8B Math18-Lecture8-B00-before.pdf Math18-Lecture8-B00-after.pdf
8C Math18-Lecture8-C00-before.pdf Math18-Lecture8-C00-after.pdf
9B Math18-Lecture9-B00-before.pdf Math18-Lecture9-B00-after.pdf
9C Math18-Lecture9-C00-before.pdf Math18-Lecture9-C00-after.pdf
10B Math18-Lecture10-B00-before.pdf Math18-Lecture10-B00-after.pdf
10C Math18-Lecture10-C00-before.pdf Math18-Lecture10-C00-after.pdf
11B Math18-Lecture11-B00-before.pdf Math18-Lecture11-B00-after.pdf
11C Math18-Lecture11-C00-before.pdf Math18-Lecture11-C00-after.pdf
12B Math18-Lecture12-B00-before.pdf Math18-Lecture12-B00-after.pdf
12C Math18-Lecture12-C00-before.pdf Math18-Lecture12-C00-after.pdf
13B Math18-Lecture13-B00-before.pdf Math18-Lecture13-B00-after.pdf
13C Math18-Lecture13-C00-before.pdf Math18-Lecture13-C00-after.pdf
14B Math18-Lecture14-B00-before.pdf Math18-Lecture14-B00-after.pdf
14C Math18-Lecture14-C00-before.pdf Math18-Lecture14-C00-after.pdf
15B Math18-Lecture15-B00-before.pdf Math18-Lecture15-B00-after.pdf
15C Math18-Lecture15-C00-before.pdf Math18-Lecture15-C00-after.pdf
16B Math18-Lecture16-B00-before.pdf Math18-Lecture16-B00-after.pdf
16C Math18-Lecture16-C00-before.pdf Math18-Lecture16-C00-after.pdf
17B Math18-Lecture17-B00-before.pdf Math18-Lecture17-B00-after.pdf
17C Math18-Lecture17-C00-before.pdf Math18-Lecture17-C00-after.pdf
18B Math18-Lecture18-B00-before.pdf Math18-Lecture18-B00-after.pdf
18C Math18-Lecture18-C00-before.pdf Math18-Lecture18-C00-after.pdf
19B Math18-Lecture19-B00-before.pdf Math18-Lecture19-B00-after.pdf
19C Math18-Lecture19-C00-before.pdf Math18-Lecture19-C00-after.pdf
20B Math18-Lecture20-B00-before.pdf Math18-Lecture20-B00-after.pdf
20C Math18-Lecture20-C00-before.pdf Math18-Lecture20-C00-after.pdf
23B Math18-Lecture23-B00-before.pdf Math18-Lecture23-B00-after.pdf
23C Math18-Lecture23-C00-before.pdf Math18-Lecture23-C00-after.pdf
24B Math18-Lecture24-B00-before.pdf Math18-Lecture24-B00-after.pdf
24C Math18-Lecture24-C00-before.pdf Math18-Lecture24-C00-after.pdf
25B Math18-Lecture25-B00-before.pdf Math18-Lecture25-B00-after.pdf
25C Math18-Lecture25-C00-before.pdf Math18-Lecture25-C00-after.pdf
26B Math18-Lecture26-B00-before.pdf Math18-Lecture26-B00-after.pdf
26C Math18-Lecture26-C00-before.pdf Math18-Lecture26-C00-after.pdf
27B Math18-Lecture27-B00-before.pdf Math18-Lecture27-B00-after.pdf
27C Math18-Lecture27-C00-before.pdf Math18-Lecture27-C00-after.pdf
28B Math18-Lecture28-B00-before.pdf Math18-Lecture28-B00-after.pdf
28C Math18-Lecture28-C00-before.pdf Math18-Lecture28-C00-after.pdf