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Preface
Here are my online notes for my Algebra course that I teach here at Lamar University, although I
have to admit that it’s been years since I last taught this course.
At this point in my career I
mostly teach Calculus and Differential Equations.
Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to
learn Algebra or needing a refresher for algebra.
I’ve tried to make the notes as self contained as
possible and do not reference any book.
However, they do assume that you’ve has some
exposure to the basics of algebra at some point prior to this.
While there is some review of
exponents, factoring and graphing it is assumed that not a lot of review will be needed to remind
you how these topics work.
Here are a couple of warnings to my students who may be here to get a copy of what happened on
a day that you missed.
1.
Because I wanted to make this a fairly complete set of notes for anyone wanting to learn
algebra I have included some material that I do not usually have time to cover in class
and because this changes from semester to semester it is not noted here.
You will need to
find one of your fellow class mates to see if there is something in these notes that wasn’t
covered in class.
2.
Because I want these notes to provide some more examples for you to read through, I
don’t always work the same problems in class as those given in the notes.
Likewise, even
if I do work some of the problems in here I may work fewer problems in class than are
presented here.
3.
Sometimes questions in class will lead down paths that are not covered here.
I try to
anticipate as many of the questions as possible in writing these up, but the reality is that I
can’t anticipate all the questions.
Sometimes a very good question gets asked in class
that leads to insights that I’ve not included here.
You should always talk to someone who
was in class on the day you missed and compare these notes to their notes and see what
the differences are.
4.
This is somewhat related to the previous three items, but is important enough to merit its
own item.
THESE NOTES ARE NOT A SUBSTITUTE FOR ATTENDING CLASS!!
Using these notes as a substitute for class is liable to get you in trouble. As already noted
not everything in these notes is covered in class and often material or insights not in these
notes is covered in class.
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View Full Document More on the Augmented Matrix
In the first section in this chapter we saw that there were some special cases in the solution to
systems of two equations. We saw that there didn’t have to be a solution at all and that we could
in fact have infinitely many solutions.
In this section we are going to generalize this out to
general systems of equations and we’re going to look at how to deal with these cases when using
augmented matrices to solve a system.
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This note was uploaded on 11/12/2011 for the course MATH 101 taught by Professor Fisher during the Fall '11 term at Rutgers.
 Fall '11
 Fisher
 Differential Equations, Algebra, Equations

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