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Math 200 Linear Algebra

Course Description

This course will be an introduction to linear algebra. Our main goal for this class will be to work
our way from the concrete to the abstract. We will begin with a situation which is familiar to
you: solving small systems of linear equations. We will use this to springboard into a discussion
of matrices, solving vector equations, linear transformations, and properties of the familiar vector
space Rn. (A note on notation: R1 is the real line, R2 is the real plane, R3 is three-dimensional
space, and so on.)

Once we have the basics in place for this concrete setting, we will consider abstract vector spaces
and see how the topics we have studied in Rn apply to vector spaces in general. While in the
general vector space setting, we will consider eigenvalues and eigenvectors as well as inner products
and orthogonality.

As we work our way through the course, our other goal will be to work on writing proofs. For
many of you, this will be the first time you have written mature mathematical proofs so this course
serves as a place for your to try your hand at it and begin to work on developing your style.


We will work from Linear Algebra and Its Applications, 3rd ed., update by David C. Lay.
Note that the third edition update comes with a CD that contains the Student Study Guide for
the text. I highly encourage you to make use of this resource.


Homework assignments will be posted on the course website.

Homework will be assigned after class each day and will be due at the start of the following class.
Please write neatly and staple your work. Working problems is the only way to really learn
math so therefore I strongly encourage you to work carefully through each exercise in
order to develop intuition for the subject. You will find that by being diligent about doing your
homework, you will be much more well-prepared for the exams. In a typical non-exam week, you
should expect to spend about two to three hours of work outside of class for every hour spent in

Homework is graded on a 0-1-2 scale. A zero is given for little or no work shown (even if the answer
is correct), a one is given if the exercise is attempted but incomplete, and a two is given for a
mostly or totally correct answer.

Note that no late homework will be accepted, even for reasons of mild illness. Late homework
will receive a score of zero. You may however, hand in homework early if a conflict arises. I will
drop your lowest three homework scores when I calculate your final average.


There will be two midterm exams and one final exam. The midterm exams are scheduled for

Monday, March 9 at 7:30pm
Wednesday, April 15 at 7:30pm

The final exam will be scheduled by the registrar. Do not try to determine our exam date from
the "Outline" that is posted on the college website. The outline does not apply to our class.

As with homework, no late exams will be given. If you have a conflict with either midterm
exam date, please see me at least two weeks before the exam so that we can make arrangements
for you to take the exam early. Vacation plans are not a legitimate reason for arranging an early
exam so please plan to be on campus until after our final exam date.

Honor Code

You may (in fact you are encouraged to!) work together in pairs or groups while you are figuring
out homework assignments. However, your final write-up of each assignment must be your own.
Copying is considered a breach of the honor code.

You are expected to complete exams entirely on your own. All exams will be closed-book and there
will be no calculators allowed.


I will determine final grades according to whichever of the the following percentages gives the better

Exam 1 30%
Exam 2 30%
Final Exam 30%
Homework and Class Participation 10%
Exam 1 27.5%
Exam 2 27.5%
Final Exam 35%
Homework and Class Participation 10%

Tentative Schedule of Topics

Week Beginning Topics
Feb 9 Solving systems of linear equations, row reduction, vector equations
Feb 16 Matrix equation Ax = b, solution sets of linear systems (Winter Carnival)
Feb 23 Linear independence, linear transformations and matrices
Mar 2 Matrix operations, inverting matrices, characterizations of invertible matrices
Mar 9 Introduction to and properties of determinants, (Exam 1)
Mar 16 Determinants and volume, vector spaces and subspaces
Mar 23 Spring Break!
Mar 30 Null and column spaces, bases, coordinate systems
Apr 6 Dimension of a vector space, rank, change of basis
Apr 13 Markov chains, eigenvalues and eigenvectors, the characteristic equation (Exam 2)
Apr 20 Diagonalization, eigenvectors and linear transformations
Apr 27 More eigenvectors and linear transformations, inner products, orthogonality
May 4 Orthogonal sets, orthogonal projections, the Gram-Schmidt process