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In the syllabus below, FCLA refers to the official course text A First Course in Linear Algebra and Lay refers to the additional/optional text by David C. Lay (see the course info page). Since this is the first year we are using FCLA, the section numbers below may be updated as the courses progresses. Similarly, the list of recommended exercises for FCLA will be updated before each lecture.
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 tips page). Note that the answers to odd-numbered exercises in Lay can be found at the back of the text and complete solutions to some questions can be found in the study guide to the text. Complete solutions to most of the exercises in FCLA are contained in the text itself.
Lectures notes and streaming video of the lecture will be posted after each class in the table below. In addition, the video (for all lectures except the first two) is available here. If it appears that lecture notes and/or video have not been posted after a lecture, try clicking "refresh" in your browser.
| Date | Text Sections | Lecture Slides |
Video | Material | Recommended Exercises | ||
| FCLA | Lay | FCLA | Lay (3rd ed., 4th ed., both editions) | ||||
| Jan 10 | WILA | 1.1 | Lec 1 | Lec 1 | Introduction, background on sets, number sets, and logic, systems of linear equations | WILA.READ: 1, 2; SSLE.EXC: C20 | Sec 1.1: Practice Problem 3 |
| Jan 12/13 | SSLE, RREF | 1.1, 1.2 | Lec 2 | Lec 2 | Solving systems of linear equations, echelon forms | SSLE.EXC: C30–C50, T20 | Sec 1.1: 1, 3, 11, 13, 15, 19; Sec 1.2: 1 |
| Jan 17 | RREF, TSS | 1.2 | Lec 3 | Lec 3 | Row reduction algorithm, general solutions of linear systems | RREF.EXC: C05, C30–C33, M45 | Sec 1.2: 3, 5, 7, 9, 11, 13 |
| Jan 19/20 | TSS | 1.2 | Lec 4 | Lec 4 | General solutions of linear systems (cont.), existence and uniqueness of solutions | TSS.EXC: C21–C28, M51–M57 | Sec 1.2: 15, 17–21, 23–26 |
| Jan 24 | VO, LC.LC, SS.SSV | 1.3 | Lec 5 | Lec 5 | Vectors, vector equations, linear combinations | VO.EXC: C10–C15; LC.EXC: C21; SS.EXC: C40–C45 | Sec 1.3: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 |
| Jan 26/27 | RREF.MVNSE | 1.4, 1.6 | Lec 6 | Lec 6 | Matrix equations, application: network/traffic flow | LC.EXC: C22–C41, M10; SS.EXC: C40–C45;
Network exercises (Solutions) |
Sec 1.4: 1, 3, 5, 7, 9, 11, 13, 17, 19; Sec 1.6: 11, 13, 15 |
| Jan 31 | HSE, LC | 1.5 | Lec 7 | Lec 7 | Solution sets of linear systems, vector parametric descriptions | HSE.EXC: C10, C21–C27, T10; LC.EXC: C21–C41, M10 | Sec 1.5: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 |
| Feb 2/3 | LI | 1.7 | Lec 8 | Lec 8 | Linear independence | LI.EXC: C20–C25, C50 | Sec 1.7: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 22, 27, 33, 35, 37 |
| Feb 7 | MO, MM | 2.1 | Lec 9 | Lec 9 | Matrix addition, scalar multiplication, matrix multiplication | MO.EXC: C10 (1,2,5,6), C11–C14; MM.EXC: C20–C30 | Sec 2.1: 1, 3, 7, 9, 11, 13 |
| Feb 9/10 | Midterm Exam | Covers Lectures 1–8. | |||||
| Feb 14 | MISLE, MINM | 2.1, 2.2 | Lec 10 | Lec 10 | Transposes, matrix inverses | MO.EXC: C10 (3,4,7,8,9); MISLE.EXC: C21–C25 | Sec 2.1: 15, 23, 27; Sec 2.2: 1, 3, 5, 9, 13, 17, 18 |
| Feb 16/17 | MISLE, MINM | 2.2, 2.3 | Lec 11 | Lec 11 | Matrix inverses (cont.) | MISLE.EXC: C16–C19, C26–C42; MINM.EXC: C40 | Sec 2.1: 17; Sec 2.2: 19, 20, 23, 29, 31, 32, 35; Sec 2.3: 1, 3, 5, 7 |
| Feb 20–24 | |||||||
| Feb 28 | See lecture slides | 2.6 | Lec 12 | Lec 12 | Leontief Input-Output Model | Input-Output Model exercises (Solutions) | Sec 2.6: 1, 3, 5, 7, 9 |
| Mar 1/2 | S, LISS, B | 2.8 | Lec 13 | Lec 13 | Subspaces of Rn, bases | S.EXC: C15–C17, C25, C26 (replace C by R) | Sec 2.8: 7, 9, 11, 15, 17, 19, 21, 22; Sec 4.1: 3, 9, 11, 13 |
| Mar 6 | D, PD, HSE.NSM | 2.8, 2.9 | Lec 14 | Lec 14 | Dimension, rank, column space, null space | D.EXC: C20, C21 (replace C by R), C30–C37; HSE.EXC: C20, C30, C31 | Sec 2.9: 9, 11, 13, 15, 17, 19, 21, 23; Sec 4.2: 1, 3, 5, 15, 17, 19 |
| Mar 8/9 | DM | 3.1 | Lec 15 | Lec 15 | Determinants | DM.EXC: C21–C30, M10–M15 | Sec 3.1: 1, 3, 5, 7, 9, 11, 13, 19, 21, 23, 37 |
| Mar 13 | PDM | 3.2 | Lec 16 | Lec 16 | Properties of determinants | PDM.EXC: C30, M30 | Sec 3.2: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 39 |
| Mar 15/16 | CNO | Appendix B | Lec 17 | Lec 17 | Complex Numbers | Exercises (Answers) | |
| Mar 20 | EE, PEE | 5.1 | Lec 18 | Lec 18 | Eigenvectors and eigenvalues Teaching Evaluations |
None until next lecture. | Sec 5.1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 26 |
| Mar 22/23 | Midterm Exam | Covers Lectures 1–16. | |||||
| Mar 27 | EE, PEE | 5.2 | Lec 19 | Lec 19 | The characteristic equation | EE.EXC: C10–C27 | Sec 5.2: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 |
| Mar 29/30 | SD | 5.3 | Lec 20 | Lec 20 | Diagonalization | SD.EXC: C20, C21, T15–T17 | Sec 5.3: 1, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 19 |
| Apr 3 | See lecture slides (Example) | 1.10, 4.9 | Lec 21 | Lec 21 | Difference equations, Markov chains, Google PageRank | Markov Chain exercises (Solutions) | Sec 1.10: 9; Sec 4.9: 1, 3, 5, 7, 9, 11, 13 |
| April 5/10 | N/A | Lec 22 | Lec 22 | Review | |||