Linear Algebra

For guidance, in the table of contents I have marked some subsections as
optional if, in my opinion, some instructors will pass over them in favor of
spending more time elsewhere. These subsections can be dropped or added, as
desired. You might also adjust the length of your study by picking one or two
Topics that appeal to you from the end of each chapter. You’ll probably get
more out of these if you have access to computer software that can do the big
calculations.
Do many exercises. (The answers are available.) I have marked a good sample
with �’s. Be warned about the exercises, however, that few inexperienced
people can write correct proofs. Try to find a knowledgeable person to work
with you on this aspect of the material.
Finally, if I may, a caution: I cannot overemphasize how much the statement
(which I sometimes hear), “I understand the material, but it’s only that I can’t
do any of the problems.” reveals a lack of understanding of what we are up
to. Being able to do particular things with the ideas is the entire point. The
quote below expresses this sentiment admirably, and captures the essence of
this book’s approach. It states what I believe is the key to both the beauty and
the power of mathematics and the sciences in general, and of linear algebra in
particular.
I know of no better tactic
than the illustration of exciting principles
by well-chosen particulars.
–Stephen Jay Gould
Jim Hefferon
Saint Michael’s College
Colchester, Vermont USA
jim@joshua.smcvt.edu
April 20, 2000
Author’s Note. Inventing a good exercise, one that enlightens as well as tests,
is a creative act, and hard work (at least half of the the effort on this text
has gone into exercises and solutions). The inventor deserves recognition. But,
somehow, the tradition in texts has been to not give attributions for questions.
I have changed that here where I was sure of the source. I would greatly appreciate
hearing from anyone who can help me to correctly attribute others of the
questions. They will be incorporated into later versions of this book.
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