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 | |||
Jan 9 | WILA | Lec 1 | Solving systems of linear equations, echelon forms. |
WILA: Reading Questions 1, 2. SSLE: C30. |
Jan 12 | SSLE, RREF | Lec 2 | Row reduction algorithm, general solutions of linear systems. |
SSLE: C31–C50. RREF: C10–C19. |
Jan 16 | RREF, TSS | Lec 3 | General solutions of linear systems (cont.), existence and uniqueness of solutions, vectors. |
RREF: C30–C33 TSS: C21–C28, M51–M57. |
Jan 19 | VO, LC, SS | Lec 4 | Vector equations, linear combinations, span. | VO: C10–C15.
LC: C21. SS: C40–C45. |
Jan 23 | RREF | Lec 5 | Matrix equations, network flow. | LC: C22–C41, M10. SS: C40–C45. Network flow |
Jan 26 | HSE, LC | Lec 6 | Solution sets of linear systems, vector parametric descriptions. |
HSE: C10, C21–C27, T10. LC: C21–C41, M10. |
Jan 30 | LI | Lec 7 | Linear independence. | LI: C20–C25, C50. |
Feb 2 | First Midterm Exam Based on Lectures 1–6 |
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Feb 6 | MO, MM | Lec 8 | Matrix addition, scalar multiplication, matrix multiplication. | MO: C10 (1,2,5,6), C11–C14. MM: C20–C30. |
Feb 9 | MISLE, MINM | Lec 9 | Transposes, matrix inverses. | MO: C10 (3,4,7,8,9). MISLE: C21–C25. |
Feb 13 | MISLE, MINM | Lec 10 | Matrix inverses (continued). | MISLE: C16–C19, C26–C42. MINM: C40. |
Feb 16 | See lecture slides | Lec 11 | Leontief Input-Output model. | |
Feb 20 | Reading Week | |||
Feb 23 | Reading Week | |||
Feb 27 | S, LISS, B | Lec 12 | Subspaces of R^{n}. | S: C15–C17, C25, C26 (replace C by R). |
Mar 2 | Second Midterm Exam Based on Lectures 1–11 |
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Mar 6 | D, PD, HSE | Lec 13 | Dimension, rank, column space, null space. | D: C20, C21 (replace C by R), C30–C37. HSE: C20, C30, C31. |
Mar 9 | DM | Lec 14 | Determinants. | DM: C21–C30, M10–M15. |
Mar 13 | PDM | Lec 15 | Properties of determinants. | PDM: C30, M30. |
Mar 16 | CNO | Lec 16 | Complex Numbers | Exercises (Answers). |
Mar 20 | EE, PEE | Lec 17 | Eigenvectors and eigenvalues. Course evaluation |
None until Lecture 18 |
Mar 23 | Third Midterm Exam Based on Lectures 1–16 |
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Mar 27 | EE, PEE | Lec 18 | The characteristic equation. | EE: C10–C27. |
Mar 30 | Good Friday | |||
Apr 3 | SD | Lec 19 | Diagonalization. | SD: C20, C21, T15–T17. |
Apr 6 | Lec 20 | Difference equations, Markov Chain. | ||
Apr 10 | Lec 21 | Review. |