Math 223 Section 101
Linear Algebra
Online Course Material 


Hope you had a great summer. I look forward to another chance to teach this course.

This is an Honours level course that both covers the material of MATH 221 and MATH 152 but adds some theoretical material. The grading standards (for me) are roughly those of MATH 221 and so some judicious scaling will be used. It will be substantially more work than MATH 221 but hopefully much more interesting.

Please note that this course cannot be taken for credit if you have already taken MATH 221 or MATH 152.

The first midterm is October 7. You will get a break with Thanksgiving.
  • Sample midterm 1 I will not post solutions but you can ask me about your solutions during office hours.  
  • The second midterm is November 9.

    I will be putting many course materials on the web in pdf format to supplement the text. The text has some excellent explanations but note that the problems tend to be much too elementary.
    The notes look authoritative when typed so be wary. They may look perfect but may still contain errors! I don't have an editor.
    I arrive most days by 9:00. I will typically be available after class in my office MATH ANNEX 1114 at 11 each day. I will have an office hour 4:30-5:30 on Thursdays in MATH ANNEX 1118 (near my office) and imagine many assignments will be due Fridays. Other office hours will be available. I do not reliably read my email from home (i.e. evenings and weekends) nor every hour at work.

  • Course Outline: grading scheme etc. 
  • Assignment 1. Due Friday September 16 Assignment 1 solutions.  
  • Assignment 2. Due Friday September 23 Assignment 2 solutions.  
  • Assignment 3. Due Friday September 30 Assignment 3 solutions.  
  • Assignment 4. Due Wednesday October 5 Assignment 4 solutions.  
  • Assignment 5. Due Friday October 21  
  • Midterm 1 Solutions.  

  • Various Notes. Often for material not in text or at least not in the order we follow.

  • 2x2 matrices from first lecture  
  • 2x2 matrices from second lecture  
  • Putnam problem from second lecture  
  • 2x2 matrices as geometric transformations and also Linear Transformations  
  • Different levels of generality.  
  • Bird populations and eigenvalues and eigenvectors.  
  • White and Blue Coordinates.  
  • Fibonacci numbers.  
  • Gaussian Elimination.  
  • Determinants.  
  • Partial Fractions.  
  • Interchanging rows 1 and 2 changes determinant by -1.  
  • Axioms for a Field and for a Vector Space.  
  • Introduction to Vector Spaces including the idea that: a vector is not a vector.  
  • Ideas of Linear Independence, spanning sets and dimension. Big important topics of MATH 223  

  • The Math Learning Centre (or MLC for short) is a space for undergraduate students to study math together, with friendly support from tutors, who are graduate and undergraduate students in the math department. The MLC is located at LSK301 and LSK302 and is open 5 days a week 11am-6pm starting September 14th. Every undergraduate student studying Math is welcome here! In the MLC, students may join the study groups if students wish so. Please note that while students are encouraged to seek help with homework, the MLC is not a place to check answers or receive solutions, rather, our aim is to aid students in becoming better learners and to develop critical thinking in a mathematical setting. For additional information please visit our website website. .

  • Matrix multiplication and some possible interpretations other than as linear transformations. Multiplication on the left is a row operation, multiplication on the right is a column operation etc. We discuss other interpretations later in the course.  
  • An interactive 2x2 matrix multiplication: A java program that allows you to move input point A around and see the output after a 2x2 matrix multiplication. The matrix entries are a,b,c,d and the java program gives you sliders to change their values if you wish. The initial data for a,b,c,d corresponds to the matrix for the fibonacci numbers. This demo was created with GeoGebra in about 1 hour with no knowledge of Java except the idea of jar files. You can play with this free software at (NOT  

  • How to slice a bagel Use edible ink.