Math 2255 - Linear Algebra I (2006/07)

Math 2255, combined with the second semester course Math 2275, form an introduction to Linear Algebra. This course is for students in mathematics, but students in physics, computer science, and economics may also find the results useful. In this course we 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.

News (Last Updated Dec. 15, 2006)

Below is a summary of what we did in class, plus any relevant news and/or information.

• Dec. 15, 2006 I have finished grading the final. You can see your mark, plus your unofficial final mark using the link Exam and Unofficial Grades. I hope you enjoyed the course, and I wish you a happy holiday! See you in the new year!
• Nov. 29, 2006 Check out your PreExam Grades Please make sure everything agrees with your records.
• Nov. 29, 2006 In our last formal lecture, I did some review questions and discussed the exam. All assignments to HWA 8 will handed back, and HWA 9 was due. You will get HWA 9 in tomorrow's class where I will do review.
• Nov. 27, 2006 I handed out the review sheet. I also finished Chapter 4. We looked at probability vectors, Markov chains, and stochastic matrices. I used MatLab to illustrate some of these ideas.
• Nov. 24, 2006 Start studying! I have added the Exam Review Sheet to the web. I will give out a hard copy in class.
• Nov. 24, 2006 We looked at Section 4.8 on linear difference equations. In particular, we studied the space of signals, which is an example of a vector space. The last MatLab assignment was due in class.
• Nov. 22, 2006 To help you study, you can try last year's final exam: 2005 Math 2255 Final Exam I will post the solutions on ERES.
• Nov. 22, 2006 I finished Section 4.7 on the change of basis matrix. I also did some problems that are like the homework questions. I also gave back the last HWA, and assigned the last HWA assignment.
• Nov. 20, 2006 I finished Section 4.6 on the Rank of a matrix, and I started Section 4.7 on change of basis matrix.
• Nov. 17, 2006 I introduced the notion of rank, and I went over the rank theorem. I also introduced the row space of a matrix.
• Nov. 15, 2006 Today I talked about dimension. You should know the basis theorem, and how to compute the dimension of Nul(A) and Col(A). I gave out the new HWA, and handed back the old assignments.
• Nov. 13, 2006 I finished Section 4.4 on coordinate bases. You should know what a coordinate map is, and an isomorphism of vector spaces. We started Section 4.5 on dimension. I also handed back MatLab 4.
• Nov. 10, 2006 I stated Section 4.4 on coordinate bases.
• Nov. 8, 2006 We finished Section 4.3. After today's class you should know how to find the basis of the null and column space of a matrix. I handed bach HWA 5, and I also gave out HWA 7 (see side column).
• Nov. 6, 2006 Today I started Section 4.3 on linearly independence and bases in a vector space. Both concepts are key in linear algebra, so make sure you understand both. Also, know the standard basis of R^n and P_n.
• Nov. 3, 2006 I finished Section 4.2 on the column space and null space of vector. You should also know how these subspaces relate to the range and kernel of a linear transformation. Also, note that MatLab 4 is due on Nov. 10, not Nov. 6 as it says in the handout.
• Nov. 1, 2006 Today we continued our discussion on vector spaces. I introduced an important subspace of a matrix, the null space. This was in Section 4.2. I also gave out the new HWA.
• Oct. 30, 2006 Today we covered Section 4.1 on vector spaces. You should know what a vector space is, and how it is an abstraction of the properties of R^n. You should also know what a subspace is, and how to determine if a set is a subspace. I also handed back the MatLab assignments.
• Oct. 27, 2006 We looked at Section 3.3 -- I introduced Cramer's rule, and discussed how the determinant computes area and volume.
• Oct. 25, 2006 I covered Section 3.2 on how row operations change the value of the determinant. Know how to use this information in order to calculate the determinant of a matrix. HWA 5 was also given out.
• Oct. 23, 2006 I went back and covered Section 2.7 (I accidently skipped it). I talked about homogeneous coordinates and its connection to computer graphics. I also handed back the first midterm.
• Oct. 20, 2006 Today we looked at Section 3.1 on determinants. You will need to know how to compute the determinant of a matrix of any size. You should also learn the trick of computing 3 x 3 matrix. The midterm should be graded by Monday.
• Oct. 16, 2006 First midterm.
• Oct. 13, 2006 In today's class I introduced LU-factorization. You should know how to find the LU-factorization of a given matrix. As well, the new MatLab assignment was due, and it has now been graded.
• Oct. 11, 2006 We did Section 2.3 and Section 2.4. You should know how to use the Invertible Matrix Theorem to determine if a matrix has an inverse or not. Also, you should also know how to partition a matrix. I also added the new HWA to the web. Please note that it is not due until Nov. 1.
• Oct. 6, 2006 We covered Section 2.2 on the inverse of a matrix. After today's class you should know what the inverse of a matrix, and how to find it.
• Oct. 4, 2006 In today's class we covered Section 2.1 on matrix operations. You will need to know who to add and multiply two matrices together. As well, you will need to know what the transpose of a matrix is.
• Oct. 2, 2006 We covered Section 1.9. We showed that any linear transformation can be associated with a matrix transformation. We also discussed geometric transformations in R^2. I also introduced onto and one-to-one transformations. Know how to use the standard matrix to determine if a transformation is one-to-one or onto.
• Oct. 1, 2006 The server is working again so I can update the page. Everything is now up-dated!!
• Sept. 29, 2006 Section 1.8 on linear transformations was studied. Know what a transformation is, and what a linear transformation is. As well, know how to make linear transformations from matrices. It is also important to understand the geometry of a transformation, e.g., how a transformation "moves" a unit square in the plane.
• Sept. 27, 2006 This class looked at Section 1.7. We introduced the important notion of linear independence and dependence. Make sure you know the difference between this two ideas! I also gave out the next HWA (see to the right).
• Sept. 25, 2006 Today we considered some applications of linear algebra by studying Section 1.6. We looked at two examples: one from economics and the second from network flow.
• Sept. 22, 2006 We looked at Section 1.5 on solution sets of linear systems. Know the difference between a homogeneous and non-homogeneous system, and how to write your solutions in parametric vector form.
• Sept. 20, 2006 We discussed Section 1.4. We looked at the matrix equation Ax = b. Know what it means for the columns of a matrix to span R^n. HWA 2 was also given out (see to the right).
• Sept. 18, 2006 I covered the material of Section 1.3. Know what a vector is, how to add two together, how to find the scalar multiple of a vector, and know the geometric meaning of vectors. As well, know what it means when we talk about the span of a vector.
• Sept. 15, 2006 MatLab is working! We meet in ATAC 3002 to try out MatLab. Make sure you try all the exercies! We will have a regular class on Monday.
• Sept. 14, 2006 There has been some problems with MatLab in ATAC 3002. The computer people are working on it, and hopefully it will ready by tomorrow for class. If it is not ready for class, we will instead have a lecture in our regular room. I will send you an email and update this webpage sometime before 11 AM tomorrow to tell you what is happening!
• Sept. 13, 2006 I finished Section 1.2 on row reduction. I gave a detailed description of the row reduction algorithm. I also introduced the notion of a pivot position and pivot column. You should know how to use the pivots to determine if a system of linear equations is consistent or inconsistent, and if it is consistent, whether it has a unique solution or an infinite number of solution. The first homework assignment was given out. On Friday, we will meet in ATAC 3002.
• Sept. 11, 2006 I gave examples of an inconsistent system and a system with an infinite number of solutions. You should also know what a echelon matrix and row reduced echelon matrix is. I also added the first homework assignment.
• Sept. 8, 2006 Today was the first day of class. After going over the course information sheet, I gave a lecture on Section 1.1. You should know what we mean by a linear equation, a system of linear equations, a solution set, and a consistent and inconsistent system.
• Sept. 3, 2006 I added information about the MatLab assignments.
• August 14, 2006 Web page set up. See you first day of class!