MATH2300
Linear Algebra II

• Final Grades (pdf)
• Note these are technically unofficial until you see them on Aurora.

• ROASS (pdf)
• Assignment & Test Info (pdf)
• Honesty Declaration (pdf)
• Forum: forum.robertborgersen.info
• Contact Information
  • Robert Borgersen
  • Office: 425 Machray Hall, Ph: 474-9791, E: borgersen2008@gmail.com
  • Office Hours: M 12:30-1:30pm, W 10:30-11:30am, R 8:30-10:00am

The final grades are posted above. Have a great summer everyone, and thanks for the great term! -Rob I will be in my office today (until 3:30pm) and tomorrow between 8:30am and 3pm marking, and if you would like to ask a question or two you are welcome to drop by. Friday I will not be available. -Rob Correction: I have a dentist appointment Thursday from 12-1 on campus, so I will be gone during that time. The 2300 Final Exam is 3 hours and has a total of 12 questions for 126 marks (though the test will be marked as if it were out of 120 to essentially give 6 bonus marks).

• Question 1 is 10 short answer questions worth 2 marks each covering the entire course.
• Question 2 (6 marks) is a short answer question covering eigenvalues.
• Question 3 (12 marks) is the beginning of the long answer questions, and covers Vector Spaces. Questions 4 (6 marks) and 5 (8 marks) cover linear transformations. Question 6 (12 marks) covers eigenvectors and diagonalization. Question 7 (14 marks) tests the Gram-Schmidt process.
• Question 8 (10 marks) is the beginning of the general proof questions. Questions 8, 9, and 10 (10 marks each) are a vector space proof, linear transformation proof, and an eigenvalue/vector proof respectively. Questions 11 (8 marks) and 12 (10 marks) are proofs involving Inner Product spaces.
• You are provided with 2 pages of scrap paper, as well as a sheet with the axioms of a vector space on it.

Good luck! -Rob Please download the new version available below. -Rob See below. -Rob Assignment 5 is due April 9th, 2010. It is to be handed in to a box just outside the door of my office BEFORE 1:30pm. -Rob See below. -Rob See below. -Rob Due one week from today (March 23rd) in class by the end of class with a signed honesty declaration. -Rob Due to a committment off campus, my office hours will be cancelled this Wednesday (March 17th). -Rob I have compiled all the marks together (including test 2) to give you an idea of where you are at. This will be the grade you have on the VW date (as there is nothing more to get back before then). The last few columns show the average you must get on ALL REMAINING MARKS (2 more assignments and final) in order to get a desired grade (50, 60, etc). I hope someone finds this helpful. -Rob Term Test 2 will cover everything up to and including what was done in the lecture on March 4th. This includes everything in the course up to and including basic geometric linear transformations. The majority of the test will specifically test the content in Chapter 8 (Linear Transformations), but some of the later concepts in Chapter 5 (Vector Spaces) will be tested as well (e.g. row space, column space, etc). The test will essentially be the same format as the last test: TF questions and long answer questions, but with one change: the true and false questions will be worth 1 mark each, rather than 2 (they will still be marked right minus wrong and so if you are not sure of your answer, leave it blank). The test will be 75 minutes long. If there are any questions, please let me know. -Rob I found some time and put some solutions for all the harder theorems on linear transformations. The file with the solutions in it has been updated with solutions for the linear transformation theorems. If there are any questions, please either post them in the forum, or let me know. -Rob I managed to make up a list of some proofs from classes, assignments, and old assignments, that are all very testable questions. I appended them to the already existing list of sample proofs. No solutions are available, and I will not guarantee to produce any of them before the test. If you have any questions, contact me for help as soon as possible and I will see what I can do with you. Also I have updated the forum with some questions / solutions, so please check that out. -Rob Solutions to assignment 3 are posted below. -Rob As discussed in class, I have created a forum to go with the course. It can be found at forum.robertborgersen.info. This is optional to use, but it is a place you can go to ask questions of both me and your fellow students. I want to help you all as best I can to learn the material. Hopefully this will turn out to be helpful. It'll just take a second to create a username, and then you can log in and post messages just like any other forum. -Rob I have posted assignment 3. It is due two weeks from today, and being that you have two weeks to do it, it is a little longer than normal, so don't put off starting it. -Rob The test and test solutions are posted below. They will be returned marked to you by next Thursday. -Rob Apologies for not getting these up sooner. They are essentially complete, but to make sure I got them up tonight, I left out some of the more tedious calculations. I hope they are of use to someone this late. Note that I do have office hours first thing in the morning, so you are welcome to come by. -Rob I have found/created the following that may be useful to you in studying.

• A suggested homework page I created for a previous version of this course.
• The textbook for this course using when teaching it through distance education. I taught this course in an online version a few years ago and this was the text book we used. It is referenced in the suggested homework document.
• Sample videos discussing Vector Spaces, Subspaces, and linear combinations and span. These videos were made for my class when I did the online version of this class.
• A sample proofs document as requested by a student in the class. This document is made up of proofs from old exams and proofs from my lecture notes. I have tried to provide proofs for as many as I could, but time has kept me from making proofs to all of them. If you have trouble with any of them, let me know.
• A list of common mistakes made while learning to write proofs
• A collection of old exams. Some of these old exams are from this course, some from the honours version of this course. They are provided for information purposes only, and without solutions. There is no guarantee the exam(s) in this course will be anything like these exams--notation may be different, and in the case of the honours version, the content may be very different.

Links to these items are found below. -Rob The details for test #1 are as follows: It is a 75 minute test held in class time on February 4, 2010. It covers vector spaces up to and including basis and dimension. There are 10 True/False questions (worth 2 marks each) and 5 long answer questions (worth 10 marks each). The True/False questions will be marked right minus wrong, and no part marks will be given. For the long answer questions, all work must be shown, and in some cases, the entire mark may be based upon the work rather than the final answer. All the vector space axioms are provided for you on the test. No notes, texts, calculators, or other electronic devices are to be present during the exam. Do not bring any paper with you into the exam, as scrap paper will be provided for you. The exam can be written in either pen or pencil, but a pen must be used to sign your name on the first page. -Rob I managed to find some notes written by Dr. David Gunderson that cover a) proofs of the equivilance of a number of properties to show that a matrix is invertible, and b) some review pages for working with vectors in Rn. They are essentially review at this point. If you find them useful, great. If not, that's fine too. -Rob On Thursday January 21, when the assignments were due, after everyone left it was apparent someone had taken my textbook. This textbook is property of the department of mathematics (as it indicates on the side of the book). Please check if you picked it up by mistake, and if you did, please return it to me as soon as possible. -Rob Assignment 2 is due one week from today, February 2, 2010, in class, by the end of class, with a signed honesty declaration. -Rob See below. -Rob An employee of the bookstore emailed me and told me that as of noon yesterday, Anton was on the shelves in the bookstore ready to go. If you haven't picked it up yet, please do. -Rob A copy of the 8th edition of Anton is available right now in the science library (2nd floor of Machray Hall) for one hour reserve. In case you need it, the call number is QA 184 A57 2000. A copy of the 9th edition will be available by Tuesday next week at the latest (note there is very little difference between the 8th and 9th editions). Both will be on 1 hour reserve, so if you come in and it is not available, it should be back within an hour (Note that I would prefer a longer reserve time period, but it is out of my control--I would suggest you photocopy whatever you need out of it when you get it). -Rob Due to students having trouble getting hold of the text book, assignment one has been postponed and is now due on Thursday, January 21st. It is due in class by the end of class with a signed honesty declaration. -Rob I have posted assignment 1 below. It is due in class by the end of class on January 19th, 2010. Make sure to include a signed honesty declaration with your assignment. -Rob So apparently there was a mix up and the text book for the course was never ordered. To make things easier, we will use Anton as the main text book for the class since a number of people already have it, and it is in the bookstore already (though they are ordering more in case they run out). Note that this will invalidate some of the details in the course outline and assignment/test document since they were based on the outline of Roman. -Rob Welcome to the official website for MATH 2300, Winter 2010, at the University of Manitoba. Students are expected to check this website regularly for important updates.

• Honesty Declaration (pdf)
• Assignment 1 (pdf)
• DUE DATE CHANGED: Now due Thursday, January 21st, in class by the end of class.
• Assignment 1 Solutions (pdf)
• Assignment 2 (pdf)
• Assignment 2 Solutions (pdf)
• Test 1 (pdf)
• Test 1 Solutions (pdf)
• Assignment 3 (pdf)
• Assignment 3 Solutions (pdf)
• Assignment 4 (pdf)
• Test 2 (pdf)
• Test 2 Solutions (pdf)
• Assignment 4 Solutions (pdf)
• Assignment 5 (pdf)
• Assignment 5 Solutions (pdf)

The following worksheets are entirely VOLUNTARY, and are meant to help with learning the material of this course as well as material that you are assumed to know in this class.

• nothing yet...