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
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
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 Rn. S: C15–C17, C25, C26 (replace C by R).
Mar 2     Second Midterm Exam

Based on Lectures 1–11
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
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.