In the syllabus below, section and exercise numbers refer to the official course text A First Course in Linear Algebra. Section numbers and recommended exercises for the optional text by Lay (see the course info page) can be downloaded here.

Partial lecture slides (for following along in class) will be posted before each lecture. Full lecture slides and streaming video of the lecture will be posted after each class (click on the links in the syllabus below).

Questions on the midterm and final exams will be similar to the recommended exercises. Thus, students are strongly encouraged to work through enough of the recommended exercises until they have thoroughly mastered the material. Since it is very important to keep up with the pace of the course, students should work on the exercises associated to a given lecture before the next lecture. Keep in mind that there are many resources available to help you if you are having difficulties (see the resources page). Complete solutions to most of the exercises are contained in the text itself.

Date Text Sections Video Slides Material Recommended Exercises
N/A N/A N/A Full Background on sets, notation and logic N/A
Jan 13 WILA Lec 1 Partial, Full Introduction, systems of linear equations, solution sets, row operations WILA: Reading Questions 1, 2; SSLE: C20
Jan 16 SSLE, RREF Lec 2 Partial, Full Solving systems of linear equations, echelon forms, row reduction SSLE: C30–C50, T20
Jan 20 RREF, TSS Lec 3 Partial, Full General solutions of linear systems, existence and uniqueness of solutions RREF: C05, C30–C33, M45; TSS: C21–C28, M51–M57
Jan 23 VO, LC.LC, SS.SSV Lec 4 Partial, Full Vectors, vector equations, linear combinations VO: C10–C15; LC: C21; SS: C40–C45
Jan 27 RREF.MVNSE Lec 5 Partial, Full Matrix equations, application: network/traffic flow LC: C22–C41, M10; SS: C40–C45;
Network exercises (Solutions)
Jan 30 HSE, LC Lec 6 Partial, Full Solution sets of linear systems, vector parametric descriptions HSE: C10, C21–C27, T10; LC: C21–C41, M10
Feb 3 LI Lec 7 Partial, Full Linear independence LI: C20–C25, C50
Feb 6 Midterm Exam (Covers lectures 1–6)
Feb 10 MO, MM Lec 8 Partial, Full Matrix addition, scalar multiplication, matrix multiplication MO: C10 (1,2,5,6), C11–C14; MM: C20–C30
Feb 13 MISLE, MINM Lec 9 Partial, Full Transposes, matrix inverses MO: C10 (3,4,7,8,9); MISLE: C21–C25
Feb 16–20
Reading break
Feb 24 MISLE, MINM Lec 10 Partial, Full Matrix inverses (cont.) MISLE: C16–C19, C26–C42; MINM: C40
Feb 27 See lecture slides Lec 11 Partial, Full Leontief Input-Output Model Input-Output Model exercises (Solutions)
Mar 3 S, LISS, B Lec 12 Partial, Full Subspaces of Rn, bases S: C15–C17, C25, C26 (replace C by R)
Mar 6 Midterm Exam (Covers lectures 1–11)
Mar 10 D, PD, HSE.NSM Lec 13 Partial, Full Dimension, rank, column space, null space D: C20, C21 (replace C by R), C30–C37; HSE: C20, C30, C31
Mar 13 DM Lec 14 Partial, Full Determinants DM: C21–C30, M10–M15
Mar 17 PDM Lec 15 Partial, Full Properties of determinants PDM: C30, M30
Mar 20 CNO Lec 16 Partial, Full Complex Numbers Exercises (Answers)
Mar 24 EE, PEE Lec 17 Partial, Full Course evaluations. Eigenvectors and eigenvalues None until next lecture.
Mar 27 Midterm Exam (Covers lectures 1–16)
Mar 31 EE, PEE Lec 18 Partial, Full The characteristic equation EE: C10–C27
Apr 7 SD Lec 19 Partial, Full Diagonalization SD: C20, C21, T15–T17
Apr 10 See lecture slides (Example) Lec 20 Partial, Full Difference equations, Markov chains, Google PageRank Markov Chain exercises (Solutions)
April 14 N/A Lec 21 Full Review