Since it is very important to keep up with the pace of the course, students should work on the recommended exercises of every lecture before the following lecture. Questions on the midterm and final exams will be similar to the recommended exercises. Thus, students are strongly encouraged to work through all of the recommended exercises.
To see the link to the list of exercises, you should usually scroll down to the bottom of the HTML. Clicking on the link will open a minipage which contains the exercises as well as solutions to a.
If you are having difficulty with solving the exercises, you can seek guidance at the Math Help Centre or during the professor's office hours.
Lecture slides will be posted on this page as the course unfolds. The links to lecture videos will be posted on Blackboard Learn.
Date | Section | Notes | Topics | Recommended Exercises |
Background on sets, notation, and logic. | N/A | |||
Sept 6 | WILA | Lec 1 | Solving systems of linear equations, echelon forms. |
WILA: Reading Questions 1, 2. SSLE: C30. |
Sept 11 | SSLE, RREF | Lec 2 | Row reduction algorithm, general solutions of linear systems. |
SSLE: C31–C50. RREF: C10–C19. |
Sept 13 | RREF, TSS | Lec 3 | General solutions of linear systems (cont.), existence and uniqueness of solutions, vectors. |
RREF: C30–C33 TSS: C21–C28, M51–M57. |
Sept 18 | VO, LC, SS | Lec 4 | Vector equations, linear combinations, span. | VO: C10–C15.
LC: C21. SS: C40–C45. |
Sept 20 | RREF | Lec 5 | Matrix equations, network flow. | LC: C22–C41, M10. SS: C40–C45. Network flow |
Sept 25 | HSE, LC | Lec 6 | Solution sets of linear systems, vector parametric descriptions. |
HSE: C10, C21–C27, T10. LC: C21–C41, M10. |
Sept 27 | LI | Lec 7 | Linear independence. | LI: C20–C25, C50. |
Oct 2 | First Midterm Exam Based on Lectures 1–6 |
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Oct 4 | MO, MM | Lec 8 | Matrix addition, scalar multiplication, matrix multiplication. | MO: C10 (1,2,5,6), C11–C14. MM: C20–C30. |
Oct 9 | MISLE, MINM | Lec 9 | Transposes, matrix inverses. | MO: C10 (3,4,7,8,9). MISLE: C21–C25. |
Oct 11 | MISLE, MINM | Lec 10 | Matrix inverses (continued). | MISLE: C16–C19, C26–C42. MINM: C40. |
Oct 16 | See lecture slides | Lec 11 | Leontief Input-Output model. | |
Oct 18 | S, LISS, B | Lec 12 | Subspaces of R^{n}. | S: C15–C17, C25, C26 (replace C by R). |
Oct 23 | Reading Week | |||
Oct 25 | Reading Week | |||
Oct 30 | Second Midterm Exam Based on Lectures 1–11 |
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Nov 1 | D, PD, HSE | Lec 13 | Dimension, rank, column space, null space. | D: C20, C21 (replace C by R), C30–C37. HSE: C20, C30, C31. |
Nov 6 | DM | Lec 14 | Determinants. | DM: C21–C30, M10–M15. |
Nov 8 | PDM | Lec 15 | Properties of determinants. | PDM: C30, M30. |
Nov 13 | CNO | Lec 16 | Complex Numbers | Exercises (Answers). |
Nov 15 | EE, PEE | Lec 17 | Eigenvectors and eigenvalues. Course evaluation |
None until Lecture 18 |
Nov 20 | Third Midterm Exam Based on Lectures 1–16 |
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Nov 22 | EE, PEE | Lec 18 | The characteristic equation. | EE: C10–C27. |
Nov 27 | SD | Lec 19 | Diagonalization. | SD: C20, C21, T15–T17. |
Nov 29 | Lec 20 | Difference equations, Markov Chain. | ||
Dec 4 | Lec 21 | Review. |