Math 223 Section 101
Linear Algebra
Online Course Material 

NEWS
Our final exam has been scheduled for December 19 from 3:30-6:30. The room has yet to be announced.

The midterm November 13 will have only 54 minutes and must stop promptly because the next class has a midterm (as for our first midterm). It will not include Complex numbers

The midterm October 9 will have only 54 minutes and must stop promptly because the next class has a midterm. You will get a break with Thanksgiving and then there will be no assignment due next week.

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.

I will be putting course materials on the web in pdf format to supplement the text. The text has some excellent explanations but 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. Obviously I'll have to arrive a little earlier than that for teaching! I have an office hour 4-5 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 Sept 18. Solutions. 
  • Assignment 2. due Friday Sept 25. Solutions. Note office hours 5-6 on Thursday in Math Annex 1118. 
  • Assignment 3. due Friday Oct 2. Solutions. 
  • Assignment 4. due Wednesday Oct 7. Solutions. 
  • Midterm 1 solutions from Friday Oct 9.  
  • Assignment 5. due Friday Oct 23. Solutions.  
  • Assignment 6. due Friday Oct 30. Solutions.  
  • Assignment 7. due Friday Nov 6. Solutions.  
  • Midterm 2 solutions from Friday Oct 9.  
  • Assignment 8. due Friday Nov 20. Solutions.  
  • Assignment 9. due Friday Nov 20. Solutions.  


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

  • 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.  
  • Lecture notes for Sept. 9 Some of what was covered in class as we introduced 2x2 matrices..  
  • Lecture notes for Sept. 11 Some of what was covered in class as we introduced 2x2 matrices..  
  • Putnam problem from Sept. 11 Of course I donŐt expect you to solve such problems.  
  • Lecture notes from Sept. 14 .  
  • Lecture notes from Sept. 16 .  
  • Ideas about levels of generality.  
  • Lecture notes from Sept. 18 .  
  • Notes on Induction  
  • White Blue coordinates, Lecture notes from Sept. 21  
  • Fibonacci numbers, Lecture notes from Sept. 21.  
  • Gaussian Elimination, Lecture notes from Sept. 23,25.  
  • Determinants, Lecture notes from Sept. 30, Oct 2,5.  
  • Proof, that interchanging row 1 and row 2 change determinant sign. Lecture notes from Oct 2.  
  • Partial Fractions Lecture notes from Oct 7.  
  • Axioms for a Field and for a Vector Space from Oct 14 lecture. some additional remarks about Vector Spaces including `A vector is not a vector` comment.  
  • Row and Column Space and Rank of a matrix from Oct 21,23 lectures.  
  • Coordinates and Change of Basis from Oct 26 lecture.  
  • Systems of Differential Equations from Oct 30, Nov 2, Nov 4 lectures.  
  • Notes from Nov 4.  
  • Notes from Nov 6.  
  • Notes from Nov 9. This material would not be testable as a whole but of course pieces of this are standard material in the course and so testable. I hope you enjoy such trips to the Opera.  
  • Notes on Induction  
  • Geometry and vectors From Nov 16 
  • Equiangular Lines from Nov 18 
  • Orthogonal Vector Spaces from Nov 20 
  • Symmetric and Hermitian Matrices. from Nov 27/30. The computer should be used for Gram-Schmidt process on complex vectors!  
  • The Petersen Graph and a Graph Decomposition Problem. from Dec 2. The computer should be used for Gram-Schmidt process on complex vectors!  
  • Some pictures from plotting 100 points that are relatively evenly spaced on a sphere Back points, Front points, All points. The idea is how to obtain the rotation matrix by 10 degrees around an arbitrary axis.  
  • A list of topics. May be helpful when reviewing to remind you of some of the ideas/concepts presented in class.  
  • Sample midterm 1 This sample midterm is a study aid. It may be too early for you to use it profitably. I will NOT post solutions. You can come and show me your solutions and ideas if you want feedback. Reading solutions (unless you have done the problems) is not a valuable study aid in my opinion.  
  • Sample midterm 2 This sample midterm is a study aid. I will NOT post solutions. You can come and show me your solutions and ideas if you want feedback. Reading solutions (unless you have done the problems) is not a valuable study aid in my opinion.  
  • 2008 Sample Final Exam This sample exam is a study aid. It may be too early for you to use it profitably. I will NOT post solutions. You can come and show me your solutions and ideas if you want feedback. Reading solutions (unless you have done the problems) is not a valuable study aid in my opinion.  
  • 2009 Sample Final Exam This sample exam is a study aid. It may be too early for you to use it profitably. I will NOT post solutions. You can come and show me your solutions and ideas if you want feedback. Reading solutions (unless you have done the problems) is not a valuable study aid in my opinion.  
  • 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 www.geogebra.org (NOT www.geogebra.com)  


  • How to slice a bagel Use edible ink.