Math 308H, Winter 2011

Solutions to Final

Here are the solutions to today's final. Grading in progress!

Review Session

The review session is Monday from 4:30-6pm in MEB 238. There will be three 308 instructors there. We'll put up some problems to work on, roam around the room helping, and then present the solutions.

Homework for 4.8

To practice the material we covered in class on Wednesday, do 4.8 #7, #8, and #9, but let me rephrase the questions as follows: use the procedure from lecture to diagonalize each matrix A and find a formula for Aⁿx₀ in terms of the matrices D and S, as in class. Then find what (if anything) happens in the limit as n goes to infinity.

HW #7 Solutions

Here are solutions to a few problems from HW 7.

Practice Finals

I've put links to some old final exams on the exam archive. Good luck with studying and ask me if you find anything confusing.

Optional Homework Problems

Here are some suggested problems on section 4.5 and 4.7.

Quiz Solutions

Here are solutions to today's quiz. I'll have these graded and returned on Monday. Good luck to everyone, and let me know if you have any concerns.

Don't forget to fill out this survey over the weekend. We'll do review on the last day of class, and we'll also have a separate review session, and I'd like to know what you want to go over the most. As usual, it's worth one point on the homework.

Office Hours Tomorrow

My afternoon office hours tomorrow are moved to 2:45-3:45, still in ART 334. (I'm moving them because of this lecture, in case you're interested.)

Homework #7

Homework #7 is due on Friday, March 4.

Homework #5 Solutions

Here a few solutions to homework #5. Definitely check out the solution to 3.5 #40. It's a difficult problem and a good one to know.

Another thing that you might want to look at is this explanation of set notation. This isn't new stuff, but it's important to know.

Homework #6

Homework #6 is due on Wednesday, February 23.

Solutions to Midterm

Here is a copy of today's midterm, with solutions. I'll have the midterms graded and returned by Monday.

More Problems for Homework #5

Here is the full assignment for Homework #5, which is due Wednesday, February 16th. I've added problems for section 3.6, which we'll cover on Friday.

Here's a hint in problems 3.4 #1 and #2: the subspace W that they're talking about is actually the nullspace of a certain matrix. Figure out what that matrix is, and then use the technique of example 3 to find a basis for the nullspace of that matrix. There are other approaches, too, so if you have another way of doing the problem, feel free to do that instead.

Homework #4 Solutions

Here are solutions to two problems from last week's homework. They're written out much longer than your solutions should be, so please don't be intimidated by their length.

Homework #5

Important: This is not all of homework #5. More problems will be addedl ater.

Homework #5 is due Wednesday, February 16th, in two weeks.

Here's a hint in problems 3.4 #1 and #2: the subspace W that they're talking about is actually the nullspace of a certain matrix. Figure out what that matrix is, and then use the technique of example 3 to find a basis for the nullspace of that matrix. There are other approaches, too, so if you have another way of doing the problem, feel free to do that instead.

Midterm Information

Our class's midterm will be on Wednesday, February 9th. I've posted some sample midterms in my new exam archive. You can also find a link to the exam archive under Class Details, off to the right.

I've also changed my mind about one aspect of my exam policy: you are now allowed one sheet, front and back, of handwritten notes. I'd like you to hand them in with the test. Hopefully this will mean less memorization and more time to learn linear algebra.

Homework #3 Solutions

Here are solutions to a few of the trickier homework problems from last week. I encourage you to email me questions or come talk during office hours if you find any of them confusing.

Homework #4

Homework #4 is due on Wednesday, February 2.

*For problems 26 and 35 in 3.3, you only need to specify the null space of the given matrix (not the range).

Polynomial Interpolation

Here's a copy of the worksheet and solutions for today's activity. I mentioned in class that the material on the worksheet would come up again in a week or two, so let me say a bit more about that. We learned today that if you have three points of data, you can always find a parabola that goes through them. For that matter, if you have four points of data, you could find a cubic equation going through them, and if you have five points of data, you could find a quartic equation, and so on. In a few weeks, we'll learn about least-squares estimation. Imagine that you have lots of data, but since it's real-world data, it's not completely accurate. The idea with least-squares estimation is that instead of finding a line or parabola or cubic equation that exactly matches the data, you find one that best estimates it. This is a harder problem than what we did today, but a much more useful one, and in a few weeks we'll spend a class or two learning how to do this.

Catalyst Survey

This week's Catalyst survey is now up, with new and exciting questions! Don't miss the easy homework point.

Quiz Solutions

I've graded the quiz and will hand it back on Monday. Take a look at the solutions. The median score was 21 out of 30.

Homework Solutions

I've posted two solutions to problems from the last homework assignment. Check it out here. Good luck with your studying and let me know if you have any questions.

Homework #3, Advice for Quiz

Homework assignment #3 is due in class on Wednesday, January 26th.

In 1.9, #17, #18, and #25, you don't need to check your calculations, despite the problem instructions.

Our first quiz is on Friday. I'll give it in the last 25 minutes of class. It will cover sections 1.1-1.7 of the textbook. The material in chapter 1.7 is the most important, and I recommend spending most of your studying time on it. Doing the homework problems from section 1.7 is a great idea (but wait on #49--it will be more tricky than helpful). Problem #56 is a really good one to see how well you understand things.

Office Hour Change

A few people have asked me if there's anything like the Math Study Center for Math 308. The answer to this was no, but a few other 308 instructors and I have decided to make one. We've booked a room for four hours a week. At those times, you can come and work there and get your questions answered by one of us. The room is ART 334, and the hours are Tuesday, 3:30-5:30 and Thursday, 12:30-2:30. I'll be there Tuesday 4:30-5:30, but you can come at the other times too, when David Sprehn or Luke Wolcott, two 308 instructors extraordinaire, will be available to answer your questions.

I will keep doing my 9:30-10:30am Tuesday office hour, but I'm ending the Monday, 4-5pm office hour. This means that my new office hours are Tuesday, 9:30-10:30am in my office, and 4:30-5:30pm in ART 334. If you can't make it at either of those times, just send me an email and let me know what times you're free, and we'll find another time to meet.

Homework #2

Homework assignment #2 is due in class on Wednesday, January 19th. The section numbers refer to the textbook.

As always, there will be a Catalyst survey, which I'll post on Friday.

Today's Worksheet

Here's a copy of today's worksheet, and here are solutions. Please let me know if you have any questions.

Class Feedback

I've posted the weekly survey. This is a chance for you to tell me how the class is going and give me suggestions. It's also your chance to get a point on the homework with very little effort. The survey is due at the same time as the homework, at the beginning of class on Monday.

Extra Office Hour

Since the first homework assignment is due on Monday instead of the usual Wednesday, I'll be having an extra office hour this Friday, 4-5pm. Please stop by then if you'd like to talk about anything. As always, feel free to email me if you have any questions or confusions.

Homework #1

The first homework assignment is due in class on Monday, January 10th. The section numbers refer to the textbook. Please remember to staple your homework! You might lose a point if you forget.

One part of your homework will be to fill out a short online survey on Catalyst to give me a bit of feedback on how you're doing. I'll send out an email on Friday after class giving you a link to the survey, and it will be due at the start of class on Monday. The survey is not anonymous, but if you ever want to give me an anonymous suggestion, you can do it using this anonymous feedback form.

Summary of Required Work

I've posted a final copy of the syllabus, and I just wanted to give a quick summary of the required work in this class. There will be two quizzes, a midterm, and a final; you can find the dates on the right side of this page. There will also be weekly homework. Each week, I'll post the assignment. It will be due in class on the posted due date. The homework will include a short web survey that asks for some feedback on how the class is going; I'll give more specific instructions on that when I post the first homework assignment.

Welcome to Math 308H!

Hello everyone and welcome to Math 308H, Matrix Algebra. We'll be covering the basics of matrices and linear algebra. Linear algebra is a foundational subject that will come up again and again in further study in math and science. This will probably be the most conceptually difficult math class you've taken so far. It's also likely to be the most modern; nobody was really thinking about linear algebra until the 19th century, which makes it about 200 years younger than calculus. I'm particularly excited to teach it since it's important in my own research.

I'll post some more information on the class soon. Until then, please feel free to email me at tobiasj@math.washington.edu if you have any questions.