In the first of two courses, we will look at matrices and systems of linear equations; linear transformations and matrices; elementary matrix algebra; determinants; vector spaces; change of bases; real eigenvalues and eigenvectors; applications.

Last Updated: Dec. 20, 2005

• Dec. 20, 2005 I have added the UNOFFICIAL FINAL MARKS below: Math 2255 PostExam Marks Have a good Holiday!
• Dec. 3, 2005 The last homework assignment has been graded. Also, you can check your mark before the exam using the link below: Math 2255 PreExam Marks If there are any corrections, please let me know as soon as possible.
• Nov. 30, 2005 Today's class was review. I did some questions from last year's final exam. I also discussed the format of the exam.
• Nov. 28, 2005 We discussed Section 4.9 on Markov Chains. You should know the definition of a probability vector, stochastic matrix, an equilibrium vector, and how to find such a vector. My office hours will be cancelled this week since I will be out of town. However, I will in my office most of Thursday and Friday.
• Nov. 25, 2005 I finished Section 4.7 on change of basis. You should be able to do problems like the ones discussed in class. As well, I handed out the final exam review sheet.
• Nov. 23, 2005 Final exam information sheet was added to the web. Only two weeks to the final exam!!
• Nov. 23, 2005 We finished Section 4.6 on rank. In particular, we discussed how the rank of a matrix gives us information on whether or not a matrix is invertible. We started Section 4.7 with a discussion of the change of basis. HWA 7 was handed back, HWA 8 is due today, and the last assignment, HWA9 was given out.
• Nov. 21, 2005 Today I introduced the notion of a row space of a matrix. I also talked about the rank of a matrix, and discussed the Rank Theorem. This material is from Section 4.6.
• Nov. 18, 2005 We finished Section 4.5 on dimension. You should know how to calculate the dimension of Col(A) and Nul(A). Also, know the statement of the Basis Theorem, and how to use it.
• Nov. 16, 2005 I finished Section 4.4 on coordinate systems. I began Section 4.5 on the dimension of a vector space. You should know the definition, and how to find the dimensions of subspaces.
• Nov. 14, 2005 I handed back the midterms, and we had the course evaluation. I also talked about different coordinate systems (the material of Section 4.4). Given a basis for a vector space, you should be to find the B-coordinates of any vector in that vector space.
• Nov. 11, 2005 The midterms will be handed back on Monday. We also have course evaluations on Monday. Today we finished Section 4.3 on linear independence and bases. You should know how to find the basis for a null space and column space.
• Nov. 9, 2005 We had the midterm today. Challenge Assignment 4 was also due. I also posted HWA 8 to the web.
• Nov. 7, 2005 Today we started Section 4.3 on linear independence and bases. You should know the definition of a basis, and understand the examples we did in class. Next class: midterm!
• Nov. 4, 2005 I finished Section 4.2. After today's lecture, you should know what the Column Space and Null Space of a matrix A are. Also, you should know their properties, and how these two subspaces are related to the Range and Kernel of a linear transformation.
• Nov. 2, 2005 Today we finished Section 4.1 by showing that an subset of R^n that is the span of a collection of vectors is a subspace. We also started Section 4.2 where I introduced the notion of a Null Space of a matrix.
• Oct. 31, 2005 We started Chapter 4.1 with an introduction to vector spaces and subspaces. We will continue this section and start on the next section on Wednesday's class.
• Oct. 29, 2005 I added the review sheet for the second midterm. See the lefthand column.
• Oct. 28, 2005 We finished Chapter 3 on determinants. In today's class we saw how to use Cramer's rule to find inverses and solve systems of linear equations. We also saw what the determinant tells us about a linear transformation. The next midterm will cover up until today's material.
• Oct. 26, 2005 We discussed Section 3.2 on the properties of matrices. Make sure you know how the determinant of a matrix changes as we do one of the elementary row operations.
• Oct. 24, 2005 We did Section 3.1 on determinants. Know how to compute the determinants of square matrices.
• Oct. 20, 2005 New challenge assignment added to the web.
• Note: No class on Friday, October 21.
• Oct. 19, 2005 Today we discussed Section 2.7 (we will skip 2.6) on an application to computer graphics. I discussed how one can used homogeneous coordinates to turn translations into linear transformations. HWA 4 was due in class.
• Oct. 17, 2005 We talked about LU-factorization, the topic of Section 2.5. You should be able to do examples like those discussed in class.
• Oct. 14, 2005 We discussed two sections of the textbook today -- Sections 2.3 and 2.4. You should know the statement of the invertible matrix theorm, and you should know what we mean by the block (or partition) matrix. I also handed back the midterms.
• Oct. 12, 2005 Today we had the midterm.
• Oct. 6, 2005 The assignments should be graded by Tuesday morning. I have asked the grader to put the assignments in a box outside my office so that you can pick them up. The solutions to HWA 3 should also be on ERES by late today. Also, I added the next two assignments to the web.
• Note: class is cancelled on Friday, Oct. 7
• Oct. 5, 2005 Today we discussed Section 2.2 on the inverse of a matrix. I also handed back homework assignment 2. There is no homework assignment due next week; instead, study for the midterm (next week Wednesday).
• Oct. 3, 2005 I handed out the Midterm I review sheet. We discussed Section 2.1 on operations involving matrices.
• Oct. 1, 2005 I added the Midterm I Review sheet to the webpage. It is available in the column to the left.
• Sept. 30, 2005 Today we covered Section 1.9. This is the last section of Chapter 1 that we will cover. We discussed the matrix of a linear transformation. In particular, we showed that every linear transformation arises from a matrix. We also discussed the concepts of one-to-one, and onto. You should know how to use the matrix A to decide if a linear transformation has these properties.
• Sept. 28, 2005 We covered Section 1.8 on linear transformations. You should know what a transformation is, and what a linear transformation. You should also understand how a matrix can be used to make a linear transformation. The first homework assignment was also handed back.
• Sept. 26, 2005 Today we covered the material of Section 1.7 on linear independence. You should what it means for a set of vectors to be independent (and dependent).
• Sept. 23, 2005 We discussed two applications of linear algebra -- an application to economics, and an application to networks. A third application on balancing chemical equations is found in the text book (pleae read).
• Sept. 21, 2005 We covered Section 1.5. You should know the difference between a homogeneous linear system and a non-homogeneous system. As well, you should be able to write the solution set to a system of linear equations using vector notation.
• Sept. 19, 2005 Today we went over Section 1.4 on the matrix equation Ax=b. You should be able to express a system of linear equations in the form Ax = b. Also, know what it means for the columns of a matrix to span R^n.
• Sept. 16, 2005 We discussed Section 1.3 on vectors. After today's class you should know the basic operations that can be performed on vectors (addition/scalar multiplication). Also you need to know what a linear combination of vectors is, and what the span of a set of vectors is.
• Sept. 14, 2005 Today we talked about Section 1.2 and the row reduction algorithm. At this stage, you should know how to reduce a matrix to its (reduced) echelon form. You should also know what a pivot position and pivot column are.
• Sept. 12, 2005 I gave examples of an inconsistent system of linear equations, and a consistent system with an infinite number of solutions. For three equations in three variables, you should know the geometric interpretation. Also, know the difference between echelon and row reduced echelon form.
• Sept. 9, 2005 I introduced the course. I also gave a lecture covering the general theme of the course. You should know what a system of linear equations is, the difference between a inconsitent and consistent system of linear equations, what a solution set is, and how to solve some basic system of linear equations.
• Sept. 5, 2005 Minor changes to this webpage; I added some handouts as pdf files.
• Aug. 18, 2005 Webpage was setup. Welcome!