## Math 204: Linear Algebra

```           Department of Mathematics and Computer Science
Hobart and William Smith Colleges

Fall 2020.

Instructor:  David J. Eck  (eck@hws.edu)

Syllabus:  http://math.hws.edu/eck/courses/math204_f20.html

Textbook PDF:  Linear Algebra, 4th edition, by Jim Hefferon
Supporting materials at https://hefferon.net/linearalgebra

Monday, Wednesday, Friday, 9:50–10:50 AM
Gearan Center 102: Froelich Recital Hall

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 Homework Homework 1,Due August 31, Homework 2,Due September 9, Homework 3,Due September 16, Homework 4,Due September 24, Homework 5,Due October 1,

### Sixth Week: September 28 and 30; October 2

A test is planned for Friday, October 2. An information sheet is available. The test will be given in person in class. If it is not possible for you to be in class, you should let me know.

Aside from the test, we will be finishing up Chapter Three, Section III.2, which is part of the material for the test. That section covers dimension of finite-dimensional vector spaces and the fact that every basis of a finite-dimensional vector space has the same number of elements. We will do some review for the test, and there will certainly be time for questions. If we have extra time, we will move on to new material from Chapter Two, Section III.3.

Remember that Homework 5 is due by noon on Thursday, October 1.

### Fifth Week: September 21, 23, and 25

We ended last week by introducing linear independence. We will continue that this week, and we will look at the idea of a basis of a vector space and the dimension of a vector space. A basis for a vector space is simply a subset of that vector space that spans the entire vector space and is linearly independent. This is one of the central concepts in linear algebra. The reading is Chapter Two, sections II.1, III.1, and III.2. Here is a reading guide:

### Fourth Week: September 14, 16, and 18

After a brief remark on accuracy of computation, which was promised for last week, we move on to Chapter 2, which introduces vector spaces. We have been working with vectors as columns or rows of numbers, but the general concept of vector space is more general and more abstract. We will look at the definition and some basic properties of vectors spaces, subspaces, spans, and linear combinations. The reading guides for this week are

### Third Week: September 7, 9, and 11

We will finish up Chapter One this week. The reading is Chapter One, Section III. The main topic is reduced row echelon form, but we will also be looking to get a better handle on the meaning of linear combination and how to work with it. Along the way, we will need to go over the idea of equivalence relation and the proof technique of mathematical induction. We will also be looking briefly at one of the topics at the end of the chapter, "Accuracy of Computation." For the most part, we will not cover any of the end-of-chapter topics, but I believe that it is important to be aware of the complications that arise from the fact that numerical computation and measurement are not exact.

Homework 2 is due on Wednesday. You should plan to turn in homework on time. If circumstances make that difficult for you, you should consult with me about getting an extension. Note that sample Homework 1 solutions are available. The reading guides for this week's material are:

### Second Week: August 31; September 2 and 4

For the first part of the week, we will be talking about the geometry of vectors and linear systems. I am putting more emphasis on the geometry than the book does, so some of this material is not covered in the book, or is covered later. We will also be looking at "homogeneous" linear systems and how they relate to linear systems in general. The reading from the book is Chapter One, Section I.3. There are two "reading guides" for this material:

Here is example shown in class on Monday: August 31 example

My office hours on Zoom this week will be Tuesday and Thursday, 12:30 to 2:00 and 6:30 to 8:00. You can use the Canvas Calendar feature to make an appointment during those times. Note that I will usually be in my office between classes on Monday, Wednesday, and Friday, from about 11:15 to 1:00. If you want to meet either on Zoom or in person during those times, you should arrange an appointment by email or by talking to me after class, or you should call my office (315-781-3398) to see whether I am available.

### First Week: August 24, 26, and 28

Added Aug. 27: A LaTeX example from Wednesday's class and the compiled PDF.

Welcome to the course!

You should download the PDF of the textbook and start reading Chapter One. We will try to cover most of Sections I.1, I.2, II.1, and II.2 from that chapter this week, although we will continue that material into the first part of next week. The main topics are Gauss's method for solving systems of linear equations and vectors in Rn. You are probably already familiar with the general idea of solving linear equations, but this is a good starting point for a course in linear algebra. And the sections on vectors are central to the course. I will also spend some time in class talking about the LaTeX typesetting system.

You should also carefully read the syllabus for the course!

The PDF version of the textbook is free. You will not need a printed copy, but if you would like to have one, you can order a copy from amazon.com through this link.

The first homework assignment is already available. You are encouraged to write up your solutions in LaTeX, using a free account at overleaf.com, but I will also accept handwritten work scanned to a PDF file, at least at first. For more information about submitting homework, see

http://math.hws.edu/eck/math204/f20/submitting-homework.html

I plan to post short "reading guides" for most lectures, which can be found at this link. The first three installments are

The third installment will take us into the beginning of the second week.