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
    PDF 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
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 Rn. 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
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
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.