Online
Resources for Linear Algebra (MAT 202)
Last revised: January 2007
The following web sites are directly related to the content that we cover in MAT 202. I hope you will find some of these sites helpful. I have tried to focus on sites that provide alternate explanations of the more difficult topics from linear algebra, have helpful visual representations, and/or provide additional examples.
Please let me know what you think of them, and whether there are others you find that should be included in this list. I welcome constructive feedback for improving and updating this resource list. For example, if you find that a link is no longer active, or if you find a site not on this list that you found helpful, please let me know!
Content Information:
#1 http://joshua.smcvt.edu/linalg.html/
This is a textbook written by Jim Hefferon of St.
Michael’s College. The topics are
presented in a different order than in our book (by Larson, Edwards, and Falvo),
and some of the notation is different, but there is very good content here.
From the main page, just click on the chapter you want.
Each section of every chapter ends with exercises, and you can link to
the solutions manual by clicking on any problem number.
#2 http://www.math.duke.edu/education/ccp/materials/linalg/
In order for this site to be useful, you need to already be
familiar with one of MAPLE, MATLAB, or MATHEMATICA. (MAPLE is available in the Math Building computer lab.)
The modules that would be most applicable to our course are:
Systems of Linear Equations, Matrix Arithmetic, Inverses and Elementary
Matrices, Determinants, Eigenvalues and Eigenvectors, and Linear
Transformations. Each module has
several subtopics that are explored by way of a worksheet from the application
you selected.
To navigate this site, first click on the module name you
want. Then click the “Go To
Module” button. Click on the
application you use (such as Maple or Mathematica or MatLab) to download a
worksheet for the module. The
worksheet provides an outline of the operations required in the module. You’ll have to click back and forth between the worksheet
and the instructions in the module.
This is a fun little applet to let you explore dot product
values by dragging two vectors around. Under
the “Execution” section in the left hand side, click on the Java option you
want. When the applet loads, you
can watch how the dot product value of two vectors changes by dragging the head
of one or the other vector around. Also
try dragging the side of vector (between the arc and the head), and try
dragging the arc.
This is a very nice version of the Very Important Equivalent
Conditions Theorem, including several conditions we either did not cover or did
not emphasize in class. The
two-column format is especially nice.
#5 http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/index.htm
This web site complements a linear algebra course from MIT
taught by Prof. Gilbert Strang. As
is true with most courses, the order of the content is different from our class,
but most of the main topics are included here.
On the left-hand side of the screen, you can click on
“Video Lectures” to see a video from any of his lectures.
(Of course, they are not nearly as fascinating as the lectures you
get each week, but you may still enjoy them.)
Under “Study Materials,” you can find old quizzes.
Under “Related Resources,” you can find links to a variety of other
websites. Most of these I found
difficult to manipulate, and I suspect they are difficult for students to
appreciate fully, but a lot of them have some graphics that are fun to play
with.
#6 http://mathforum.org/~klotz/Vectors/index.html
This site contains some pictures and brief descriptions of
vectors in two-space, their lengths, projections, sums, etc., corresponding to
Chapter 5 of our textbook. Click on
“Picture” instead of “Sketch” (which requires that you have the
application called Geometer’s Sketchpad).
#7 http://www.mcasco.com/p1va.html
You can see geometric displays of basic vector operations in
R2, including sums, scalar multiples, and dot products.
You can click on links to activate applets in which you can create your
own vectors and see their sums, differences, scalar multiples, and dot
products. You can ignore the cross product information at the end.
The content here corresponds to Chapter 5 of our textbook.
#8 http://wims.unice.fr/wims/wims.cgi?session=D86D9862&lang=en&module=tool%2Flinear%2Fmatrix.en
This is a matrix calculator. You enter a square matrix, and the calculator will find its
inverse, rank, eigenvalues and multiplicities, characteristic equation, etc.
#9 The following set of web pages were created by an
unidentified person. They contain
some good, basic definitions and notations.
I have included some specific topics that relate to the content in our
textbook. By looking at the home
page, you can find links to other topics, as well.
http://www.ping.be/~ping1339/vect.htm
A
brief (but good) descriptions of vector space topics.
Corresponds to Chapter 4.
http://www.ping.be/~ping1339/matr.htm
As
above, but for matrix operations (Chapter 2).
http://www.ping.be/~ping1339/lintf.htm
As
above, for linear transformations (Chapter 6).
http://www.ping.be/~ping1339/stelsels.htm
As
above, for solving systems (Chapters 1 & 2)
http://www.ping.be/~ping1339/determ.htm
- Theoretical-Part
As
above, for determinants (Chapter 3)
http://www.ping.be/~ping1339/stels2.htm
As above, but a mishmash of determinants, inverses, solutions to systems, Cramer's Rule, etc. I found this page to be the least useful for our class, but still containing some good things..
To help review:
http://www.math.northeastern.edu/~suciu/mth1230/linalg.f97.html
This is the home site for an online linear algebra course
taught by Alex Suciu at Northeastern University several years ago.
Scroll down the page a bit until you find a table with sample quizzes on
it. All of them should be good for
review purposes, except that Quiz #4 contains some topics we did not cover (but
it does have a few topics that we did cover).
The solutions are, unfortunately, difficult to understand because they
utilize the computer algebra system called Mathematica.
http://www-math.cudenver.edu/~billups/courses/ma5593/lin_alg_test.html
This sample quiz comes from an online course by Stephen
Billups at the University of Colorado at Denver. All questions except #7, 9, 11 should be good review for you.