Beezer - A First Course in Linear Algebra [GFDL] (2004).pdf

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A First Course in Linear Algebra
AFirstCourseinLinearAlgebra
AFirstCourseinLinearAlgebra
by
Robert A. Beezer
Department of Mathematics and Computer Science
University of Puget Sound
Version 2.00
Robert A. Beezer is a Professor of Mathematics at the University of Puget Sound, where he has been
on the faculty since 1984. He received a B.S. in Mathematics (with an Emphasis in Computer Science)
from the University of Santa Clara in 1978, a M.S. in Statistics from the University of Illinois at
Urbana-Champaign in 1982 and a Ph.D. in Mathematics from the University of Illinois at Urbana-
Champaign in 1984. He teaches calculus, linear algebra and abstract algebra regularly, while his
research interests include the applications of linear algebra to graph theory. His professional website is
Edition
Version 2.00.
July 16, 2008.
Publisher
Robert A. Beezer
Department of Mathematics and Computer Science
University of Puget Sound
1500 North Warner
Tacoma, Washington 98416-1043
USA
2004 by Robert A. Beezer.
c
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free
Documentation License, Version 1.2 or any later version published by the Free Software Foundation;
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is
included in the appendix entitled \GNU Free Documentation License".
The most recent version of this work can always be found at http://linear.ups.edu .
Tomywife,Pat.
Contents
Table of Contents
vi
Contributors
vii
Denitions
viii
Theorems
ix
Notation
x
Diagrams
xi
Examples
xii
Preface
xiii
Acknowledgements
xix
Part C Core
Chapter SLE Systems of Linear Equations
2
WILA What is Linear Algebra? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
LA \Linear" + \Algebra" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
AA An Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
READ Reading Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
EXC Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
SOL Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
SSLE Solving Systems of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . .
10
SLE Systems of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
PSS Possibilities for Solution Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
ESEO Equivalent Systems and Equation Operations . . . . . . . . . . . . . . . . . .
12
READ Reading Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
EXC Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
SOL Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
RREF Reduced Row-Echelon Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
MVNSE Matrix and Vector Notation for Systems of Equations . . . . . . . . . . . .
25
RO Row Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
RREF Reduced Row-Echelon Form . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
READ Reading Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
vi

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