Elementary Linear Algebra, 8th Edition.pdf

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Front Cover

Title Page

CONTENTS

Preface

1. Systems of Linear Equations

1.1 Introduction to Systems of Linear Equations

1.2 Gaussian Elimination and Gauss-Jordan Elimination

1.3 Applications of Systems of Linear Equations

Review Exercises

Projects

2. Matrices

2.1 Operations with Matrices

2.2 Properties of Matrix Operations

2.3 The Inverse of a Matrix

2.4 Elementary Matrices

2.5 Markov Chains

2.6 More applications of Matrix Operations

Review Exercises

Projects

3. Determinants

3.1 The Determinant of a Matrix

3.2 Determinants and Elementary Operations

3.3 Properties of Determinants

3.4 Applications of Determinants

Review Exercises

Projects

Cumulative Test for Chapters 1–3

4. Vector Spaces

4.1 Vectors in Rn

4.2 Vector Spaces

4.3 Subspaces of Vector Spaces

4.4 Spanning Sets and Linear Independence

4.5 Basis and Dimension

4.6 Rank of a Matrix and Systems of Linear Equations

4.7 Coordinates and Change of Basis

4.8 Applications of Vector Spaces

Review Exercises

Projects

5. Inner Product Spaces

5.1 Length and Dot Product in Rn

5.2 Inner Product Spaces

5.3 Orthonormal Bases: Gram-Schmidt Process

5.4 Mathematical Models and Least Squares Analysis

5.5 Applications of Inner Product spaces

Review Exercises

Projects

Cumulative Test for Chapters 4 and 5

6. Linear Transformations

6.1 Introduction to Linear Transformations

6.2 The Kernel and Range of a Linear Transformation

6.3 Matrices for Linear Transformations

6.4 Transition Matrices and Similarity

6.5 Applications of Linear Transformations

Review Exercises

Projects

7. Eigenvalues and Eigenvectors

7.1 Eigenvalues and Eigenvectors

7.2 Diagonalization

7.3 Symmetric Matrices and Orthogonal Diagonalization

7.4 Applications of Eigenvalues and Eigenvectors

Review Exercises

Projects

Cumulative Test for Chapters 6 and 7

APPENDIX: Mathematical Induction and Other Forms of Proofs

ANSWERS to Odd-Numbered Exercises and Tests

1.1

1.2

1.3

2.1

2.2

2.3

2.4

2.5

2.6

3.1

3.2

3.3

3.4

C 1-3

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

5.1

5.2

5.3

5.4

5.5

C 4-5

6.1

6.2

6.3

6.4

6.5

7.1

7.2

7.3

7.4

C 6-7

INDEX

Index of Applications

Properties & Procedures

INDEx OF AppLICATIONS BIOLOGY AND LIFE SCIENCES Age distribution vector, 378, 391, 392, 395 Age progression software, 180 Age transition matrix, 378, 391, 392, 395 Agriculture, 37, 50 Cosmetic surgery results simulation, 180 Duchenne muscular dystrophy, 365 Galloping speeds of animals, 276 Genetics, 365 Health care expenditures, 146 Heart rhythm analysis, 255 Hemophilia A, 365 Hereditary baldness, 365 Nutrition, 11 Population of deer, 37 of laboratory mice, 91 of rabbits, 379 of sharks, 396 of small fish, 396 Population age and growth over time, 331 Population genetics, 365 Population growth, 378, 379, 391, 392, 395, 396, 398 Predator-prey relationship, 396 Red-green color blindness, 365 Reproduction rates of deer, 103 Sex-linked inheritance, 365 Spread of a virus, 91, 93 Vitamin C content, 11 Wound healing simulation, 180 X-linked inheritance, 365 BUSINESS AND ECONOMICS Airplane allocation, 91 Borrowing money, 23 Demand, for a rechargeable power drill, 103 Demand matrix, external, 98 Economic system, 97, 98 of a small community, 103 Finance, 23 Fundraising, 92 Gasoline sales, 105 Industrial system, 102, 107 Input-output matrix, 97 Leontief input-output model(s), 97, 98, 103 Major League Baseball salaries, 107 Manufacturing models and prices, 150 production levels, 51, 105 Net profit, Microsoft, 32 Output matrix, 98 labor and material costs, 105 fast-food stand, 242 Petroleum production, 292 Profit, from crops, 50 Purchase of a product, 91 Revenue General Dynamics Corporation, 266, 276 Google, Inc., 291 Sales, 37 concession area, 42 Wal-Mart, 32 Sales promotion, 106 Satellite television service, 85, 86, 147 Software publishing, 143 telecommunications company, 242 software publishers, 143 stocks, 92 ENGINEERING AND TECHNOLOGY Aircraft design, 79 Circuit design, 322 Computer graphics, 338 Computer monitors, 190 Control system, 314 Controllability matrix, 314 Cryptography, 94–96, 102, 107 Data encryption, 94 Decoding a message, 96, 102, 107 Digital signal processing, 172 Electrical network analysis, 30, 31, 34, 37, 150 Electronic equipment, 190 Encoding a message, 95, 102, 107 Encryption key, 94 Engineering and control, 130 Error checking digit, 200 matrix, 200 Feed horn, 223 Global Positioning System, 16 Google’s Page Rank algorithm, 86 Image morphing and warping, 180 Information retrieval, 58 Internet search engine, 58 Ladder network, 322 Locating lost vessels at sea, 16 Movie special effects, 180 Network analysis, 29–34, 37 Radar, 172 Sampling, 172 Satellite dish, 223 Smart phones, 190 Televisions, 190 Wireless communications, 172 MATHEMATICS AND GEOMETRY Adjoint of a matrix, 134, 135, 142, 146, 150 Collinear points in the xy-plane, 139, 143 Conic section(s), 226, 229 general equation, 141 rotation of axes, 221–224, 226, 229, 383–385, 392, 395 Constrained optimization, 389, 390, 392, 395 Contraction in R2, 337, 341, 342 Coplanar points in space, 140, 143 Cramer’s Rule, 130, 136, 137, 142, 143, 146 Cross product of two vectors, 277–280, 288, 289, 294 Differential equation(s) linear, 218, 225, 226, 229 second order, 164 system of first order, 354, 380, 381, 391, 392, 395, 396, 398 Expansion in R2, 337, 341, 342, 345 Fibonacci sequence, 396 Fourier approximation(s), 285–287, 289, 292 Geometry of linear transformations in R2, 336–338, 341, 342, 345 linear, 282, 289, 292 Hessian matrix, 375 Jacobian, 145 Lagrange multiplier, 34 Laplace transform, 130 Least squares approximation(s), 281–284, 289 quadratic, 283, 289, 292 Linear programming, 47 Magnification in R2, 341, 342 Mathematical modeling, 273, 274, 276 Parabola passing through three points, 150 Partial fraction decomposition, 34, 37 Polynomial curve fitting, 25–28, 32, 34, 37 Quadratic form(s), 382–388, 392, 395, 398 Quadric surface, rotation of, 388, 392 Reflection in R2, 336, 341, 342, 345, 346 Relative maxima and minima, 375 Rotation Second Partials Test for relative extrema, 375 Shear in R2, 337, 338, 341, 342, 345 Taylor polynomial of degree 1, 282 Three-point form of the equation of a plane, in R2, 303, 343, 393, 397 in R3, 339, 340, 342, 345 141, 143, 146 Translation in R2, 308, 343 Triple scalar product, 288 Two-point form of the equation of a line, 139, 143, 146, 150 Unit circle, 253 Wronskian, 219, 225, 226, 229 Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

pHYSICAL SCIENCES Acoustical noise levels, 28 Airplane speed, 11 Area of a parallelogram using cross product, 279, 280, 288, 294 of a triangle using cross product, 289 using determinants, 138, 142, 146, 150 Astronomy, 27, 274 Balancing a chemical equation, 4 Beam deflection, 64, 72 Chemical changing state, 91 mixture, 37 reaction, 4 Comet landing, 141 Computational fluid dynamics, 79 Crystallography, 213 Degree of freedom, 164 Diffusion, 354 Dynamical systems, 396 Earthquake monitoring, 16 Electric and magnetic flux, 240 Flexibility matrix, 64, 72 Force matrix, 72 Geophysics, 172 Grayscale, 190 Hooke’s Law, 64 Kepler’s First Law of Planetary Motion, 141 Kirchhoff’s Laws, 30, 322 Lattice of a crystal, 213 Mass-spring system, 164, 167 Mean distance from the sun, 27, 274 Natural frequency, 164 to pull an object up a ramp, 157 Newton’s Second Law of Motion, 164 Ohm’s Law, 322 Pendulum, 225 Planetary periods, 27, 274 Primary additive colors, 190 RGB color model, 190 Stiffness matrix, 64, 72 Temperature, 34 Torque, 277 Traffic flow, 28, 33 Undamped system, 164 Unit cell, 213 end-centered monoclinic, 213 Vertical motion, 37 Volume of a parallelepiped, 288, 289, 292 of a tetrahedron, 114, 140, 143 Water flow, 33 Wind energy consumption, 103 Work, 248 SOCIAL SCIENCES AND DEMOGRApHICS Caribbean Cruise, 106 Cellular phone subscribers, 107 Consumer preference model, 85, 86, 92, 147 Final grades, 105 Grade distribution, 92 Master’s degrees awarded, 276 Politics, voting apportionment, 51 Population of consumers, 91 regions of the United States, 51 of smokers and nonsmokers, 91 United States, 32 world, 273 Population migration, 106 Smokers and nonsmokers, 91 Sports activities, 91 Super Bowl I, 36 Television watching, 91 Test scores, 108 line, 100, 103, 107, 271, 274, 276, 296 STATISTICS AND pROBABILITY Canonical regression analysis, 304 Least squares regression analysis, 99–101, 103, 107, 265, 271–276 cubic polynomial, 276 quadratic polynomial, 273, 276 Leslie matrix, 331, 378 Markov chain, 85, 86, 92, 93, 106 absorbing, 89, 90, 92, 93, 106 Multiple regression analysis, 304 Multivariate statistics, 304 State matrix, 85, 106, 147, 331 Steady state probability vector, 386 Stochastic matrices, 84–86, 91–93, 106, 331 MISCELLANEOUS Architecture, 388 Catedral Metropolitana Nossa Senhora Aparecida, 388 Chess tournament, 93 Classified documents, 106 Determining directions, 16 Dominoes, A2 Flight crew scheduling, 47 Sudoku, 120 Tips, 23 U.S. Postal Service, 200 ZIP + 4 barcode, 200 Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Elementary Linear Algebra Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Elementary Linear Algebra 8e Ron Larson The Pennsylvania State University The Behrend College Australia • Brazil • Mexico • Singapore • United Kingdom • United States Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest. Important Notice: Media content referenced within the product description or the product text may not be available in the eBook version. Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

© 2017, 2013, 2009 Cengage Learning WCN: 02-200-203 ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher. For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706. For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions. Further permissions questions can be e-mailed to permissionrequest@cengage.com. Library of Congress Control Number: 2015944033 Student Edition ISBN: 978-1-305-65800-4 Loose-leaf Edition ISBN: 978-1-305-95320-8 Cengage Learning 20 Channel Center Street Boston, MA 02210 USA Cengage Learning is a leading provider of customized learning solutions with employees residing in nearly 40 different countries and sales in more than 125 countries around the world. Find your local representative at www.cengage.com. Cengage Learning products are represented in Canada by Nelson Education, Ltd. To learn more about Cengage Learning Solutions, visit www.cengage.com. Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com. Elementary Linear Algebra Eighth Edition Ron Larson Product Director: Terry Boyle Product Manager: Richard Stratton Content Developer: Spencer Arritt Product Assistant: Kathryn Schrumpf Marketing Manager: Ana Albinson Content Project Manager: Jennifer Risden Manufacturing Planner: Doug Bertke Production Service: Larson Texts, Inc. Photo Researcher: Lumina Datamatics Text Researcher: Lumina Datamatics Text Designer: Larson Texts, Inc. Cover Designer: Larson Texts, Inc. Cover Image: Keo/Shutterstock.com Compositor: Larson Texts, Inc. Printed in the United States of America Print Number: 01 Print Year: 2015 Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

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