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 | |||||
| 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 | |