Linear Algebra and Its Applications - Study Guide
STUDY GUIDE
LINEAR ALGEBRA AND ITS APPLICATIONS
THIRD EDITION UPDATE
David C. Lay
University of Maryland – College Park
Copyright © 2006 Pearson Addison-Wesley. All rights reserved.
Reproduced by Pearson Addison-Wesley from electronic files supplied by the author. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley, 75 Arlington Street, Boston, MA 02116. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. ISBN 0-321-28066-0
1 2 3 4 5 6 BB 08 07 06 05
Copyright © 2006 Pearson Addison-Wesley. All rights reserved.
Brief Contents
INTRODUCTION HOW TO STUDY LINEAR ALGEBRA CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 CHAPTER 5 CHAPTER 6 CHAPTER 7 APPENDICES LINEAR EQUATIONS IN LINEAR ALGEBRA MATRIX ALGEBRA DETERMINANTS VECTOR SPACES EIGENVALUES AND EIGENVECTORS ORTHOGONALITY AND LEAST SQUARES SYMMETRIC MATRICES TECHNOLOGY INDEX OF PROCEDURES AND TERMS INTRODUCTION TO MATLAB NOTES FOR THE MAPLE COMPUTER ALGEBRA SYSTEM NOTES FOR THE MATHEMATICA COMPUTER ALGEBRA SYSTEM NOTES FOR THE TI-83+/86/89 GRAPHIC CALCULATORS
NOTES FOR THE HP-48G GRAPHIC CALCULATOR
Copyright © 2006 Pearson Addison-Wesley. All rights reserved.
Contents
INTRODUCTION
Technology Support vii viii Review Materials on the Web
vii
HOW TO STUDY LINEAR ALGEBRA
Strategies for Success in Linear Algebra ix
ix
CHAPTER 1
LINEAR EQUATIONS IN LINEAR ALGEBRA
1.1 1.2 1.3 1.4 Systems of Linear Systems 1-1 1-7 Row Reduction and Echelon Forms Vector Equations 1-10 1-15
The Matrix Equation Ax = b
Mastering Linear Algebra Concepts: Span 1.5 1.6 1.7 Solution Sets of Linear Systems Applications of Linear Systems Linear Independence 1-29 1-20 1-25
Mastering Linear Algebra Concepts: Linear Independence
LINEAR ALGEBRA AND ITS APPLICATIONS
THIRD EDITION UPDATE
David C. Lay
University of Maryland – College Park
Copyright © 2006 Pearson Addison-Wesley. All rights reserved.
Reproduced by Pearson Addison-Wesley from electronic files supplied by the author. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley, 75 Arlington Street, Boston, MA 02116. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. ISBN 0-321-28066-0
1 2 3 4 5 6 BB 08 07 06 05
Copyright © 2006 Pearson Addison-Wesley. All rights reserved.
Brief Contents
INTRODUCTION HOW TO STUDY LINEAR ALGEBRA CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 CHAPTER 5 CHAPTER 6 CHAPTER 7 APPENDICES LINEAR EQUATIONS IN LINEAR ALGEBRA MATRIX ALGEBRA DETERMINANTS VECTOR SPACES EIGENVALUES AND EIGENVECTORS ORTHOGONALITY AND LEAST SQUARES SYMMETRIC MATRICES TECHNOLOGY INDEX OF PROCEDURES AND TERMS INTRODUCTION TO MATLAB NOTES FOR THE MAPLE COMPUTER ALGEBRA SYSTEM NOTES FOR THE MATHEMATICA COMPUTER ALGEBRA SYSTEM NOTES FOR THE TI-83+/86/89 GRAPHIC CALCULATORS
NOTES FOR THE HP-48G GRAPHIC CALCULATOR
Copyright © 2006 Pearson Addison-Wesley. All rights reserved.
Contents
INTRODUCTION
Technology Support vii viii Review Materials on the Web
vii
HOW TO STUDY LINEAR ALGEBRA
Strategies for Success in Linear Algebra ix
ix
CHAPTER 1
LINEAR EQUATIONS IN LINEAR ALGEBRA
1.1 1.2 1.3 1.4 Systems of Linear Systems 1-1 1-7 Row Reduction and Echelon Forms Vector Equations 1-10 1-15
The Matrix Equation Ax = b
Mastering Linear Algebra Concepts: Span 1.5 1.6 1.7 Solution Sets of Linear Systems Applications of Linear Systems Linear Independence 1-29 1-20 1-25
Mastering Linear Algebra Concepts: Linear Independence