Mathematics

For a sophomore-level course in Linear Algebra.

Based on the recommendations of the Linear Algebra Curriculum Study Group, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications. Throughout the text, use of technology is encouraged. The focus is on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, and orthogonality. Although matrix-oriented, the text provides a solid coverage of vector spaces

Examples in book are accompanied by similar practice problems that enable students to test their understanding of the material  Complete solutions to the practice problems are included with the text

All computational exercises are designed so that the calculations involve “nice” numbers.

Most sections include approximately twenty true/false exercises designed to test a students understanding of the conceptual ideas in each section. (Answers to every true/false are given in the book.

Each chapter ends with a set of review exercises that provide practice with all the main topics of each chapter.

For a proof-oriented course, the authors have included a significant number of accessible exercises requiring proofs.  They are ordered according to difficulty.

Book includes wide variety of applications such as:

• Economics (the Leontief input-output model
• Electrical networks (current flow through an electrical network)
• Population change (the Leslie matrix)
• Traffic flow
• Scheduling
• Google searches

 The authors have added an appendix providing an introduction to MATLAB.

Significantly increased number of computation exercises

Complete redesign and development

PREFACE ix

TO THE STUDENT xv

CHAPTER 1 MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS 1

        1.1 Matrices and Vectors 1

        1.2 Linear Combinations, Matrix—Vector Products, and Special Matrices 11

        1.3 Systems of Linear Equations 25

        1.4 Gaussian Elimination 39

        1.5∗ Applications of Systems of Linear Equations 54

        1.6 The Span of a Set of Vectors 64

        1.7 Linear Dependence and Linear Independence 73

CHAPTER 2 MATRICES AND LINEAR TRANSFORMATIONS 90

        2.1 Matrix Multiplication 90

        2.2∗ Applications of Matrix Multiplication 101

        2.3 Invertibility and Elementary Matrices 117

        2.4 The Inverse of a Matrix 130

        2.5∗ Partitioned Matrices and Block Multiplication 141

        2.6∗ The LU Decomposition of a Matrix 147

        2.7 Linear Transformations and Matrices 162

        2.8 Composition and Invertibility of Linear Transformations 175

CHAPTER 3 DETERMINANTS 192

        3.1 Cofactor Expansion 192

        3.2 Properties of Determinants 204

CHAPTER 4 SUBSPACES AND THEIR PROPERTIES 218

        4.1 Subspaces 218

        4.2 Basis and Dimension 232

        4.3 The Dimension of Subspaces Associated with a Matrix 245

        4.4 Coordinate Systems 254

        4.5 Matrix Representations of Linear Operators 266

CHAPTER 5 EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION 282

        5.1 Eigenvalues and Eigenvectors 282

        5.2 The Characteristic Polynomial 291

        5.3 Diagonalization of Matrices 302

        5.4∗ Diagonalization of Linear Operators 314

        5.5∗ Applications of Eigenvalues 323

CHAPTER 6 ORTHOGONALITY 347

        6.1 The Geometry of Vectors 347

        6.2 Orthogonal Vectors 360

        6.3 Orthogonal Projections 374

        6.4 Least-Squares Approximations and Orthogonal Projections 388

        6.5 Orthogonal Matrices and Operators 398

        6.6 Symmetric Matrices 412

        6.7∗ Singular Value Decomposition 425

        6.8∗ Principal Component Analysis 443

        6.9∗ Rotations of R3 and Computer Graphics 452

CHAPTER 7 VECTOR SPACES 473

        7.1 Vector Spaces and Their Subspaces 473

        7.2 Linear Transformations 485

        7.3 Basis and Dimension 495

        7.4 Matrix Representations of Linear Operators 505

           7.5 Inner Product Spaces 517

APPENDICES 534

A Sets 534

B Functions 536

C Complex Numbers 539

D Matlab 544

E The Uniqueness of the Reduced Row Echelon Form 558

REFERENCES 561

ANSWERS TO SELECTED EXERCISES 562

LIST OF FREQUENTLY USED SYMBOLS 608

INDEX 609

Introductory Linear Algebra  (Mathematics)

Elementary Linear Algebra, 2/e — Lawrence Spence, Arnold Insel, and Stephen Friedberg

Embracing the recommendations of the Linear Algebra Curriculum Study Group, the authors have written a text that students will find both accessible and enlightening.  Written for a matrix-oriented course, students from a variety of disciplines can expect a greater understanding of the concepts of linear algebra. 

Starting with matrices, vectors, and systems of linear equations, the authors move towards more advanced material, including linear independence, subspaces, and bases.  The authors also encourage the use of technology, either computer software (MATLAB) or super-calculators, freeing students from tedious computations so they are better able to focus on the conceptual understanding of linear algebra. 

Lastly, students will find a variety of applications to engage their interest, demonstrated via economics, traffic flow, anthropology, Google searches, computer graphics, or music to name a few. By leveraging technology and incorporating engaging examples and numerous practice problems and exercises, this text best serves the needs of students attempting to master linear algebra. 

Instructor Solution's Manual, 2/E
Spence, Insel & Friedberg
©2008 | Prentice Hall | Paper; 244 pp | Instock
ISBN-10: 0132307529 | ISBN-13: 9780132307529

Student Solution Manual, 2/E
Spence, Insel & Friedberg
©2008 | Prentice Hall | Paper; 216 pp | Instock
ISBN-10: 013239734X | ISBN-13: 9780132397346
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Addison-Wesley's Algebra Review
Addison-Wesley
©2004 | Prentice Hall | Paper | Out of Stock
ISBN-10: 0321247086 | ISBN-13: 9780321247087

Addison-Wesley's Basic Math Review
Addison-Wesley
©2004 | Prentice Hall | Paper | Instock
ISBN-10: 0321247078 | ISBN-13: 9780321247070

Algebra Review Study Card, 2/E
D'Ippolito & Generazzo
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394739 | ISBN-13: 9780321394736
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Allied Health Study Card, 2/E
Forshier
©2006 | Prentice Hall | Study Card | Instock
ISBN-10: 0321394747 | ISBN-13: 9780321394743
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Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394763 | ISBN-13: 9780321394767
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Concept Videos: Algebra
Addison-Wesley
©2008 | Prentice Hall | Multiple Media Package | Instock
ISBN-10: 0321517199 | ISBN-13: 9780321517197

Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008 | Prentice Hall | Multiple Media Package | Instock
ISBN-10: 032151758X | ISBN-13: 9780321517586

Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997 | Prentice Hall | Paper; 195 pp | Instock
ISBN-10: 0136492037 | ISBN-13: 9780136492030
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Finite Mathematics Study Card
Addison-Wesley
©2006 | Prentice Hall | Study Card | Instock
ISBN-10: 0321374398 | ISBN-13: 9780321374394
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Flash Review Series: Algebra
Becker
©2004 | Prentice Hall | Paper | Instock
ISBN-10: 0321143094 | ISBN-13: 9780321143099
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Graphing Calculator Reference Card, 3/E
Ripley
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394755 | ISBN-13: 9780321394750
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Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Prentice Hall | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
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Interwrite Personal Response System
EduCue, Addison-Wesley & Benjamin Cummings
©2004 | Prentice Hall | Electronic Supplement | Instock
ISBN-10: 0321267354 | ISBN-13: 9780321267351

Math for Allied Health Study/Reference Card
Forshier
©2006 | Prentice Hall | Study Card; 0 pp | Out of Stock
ISBN-10: 0321336542 | ISBN-13: 9780321336545

Mathematics Spanish Glossary, 2/E
Lara & Peeples
©2000 | Prentice Hall | Paper; 48 pp | Instock
ISBN-10: 0201728966 | ISBN-13: 9780201728965
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000 | Prentice Hall | Paper | Instock
ISBN-10: 0321069188 | ISBN-13: 9780321069184
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Pearson TI Rebate Coupon $15, 2/E
Pearson Education
©2009 | Prentice Hall | Paper | Instock
ISBN-10: 0321566041 | ISBN-13: 9780321566041

Prealgebra Review Workbook
Wheel
©2006 | Prentice Hall | Paper; 300 pp | Instock
ISBN-10: 0321473329 | ISBN-13: 9780321473325
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Review of Algebra, A
Howard
©2002 | Prentice Hall | Paper; 224 pp | Instock
ISBN-10: 0201773473 | ISBN-13: 9780201773477
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Saleable Technology Bundle, 2/E
Pearson Education
©2009 | Prentice Hall | Multiple Media Package | Estimated Availability : 09/01/2008
ISBN-10: 0321561880 | ISBN-13: 9780321561886

Spanish Basic Math Study Card
Leonarte
©2007 | Prentice Hall | Study Card | Instock
ISBN-10: 0321438582 | ISBN-13: 9780321438584
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Stand-alone Access Code Tutor Center
Addison-Wesley
©2008 | Prentice Hall | Access Code Card | Instock
ISBN-10: 0201721708 | ISBN-13: 9780201721706
URL:  http://www.aw-bc.com/tutorcenter
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Understanding Linear Algebra Using MATLAB
Kleinfeld & Kleinfeld
©2001 | Prentice Hall | Paper; 210 pp | Instock
ISBN-10: 0130609455 | ISBN-13: 9780130609458

Visualizing Linear Algebra Using Maple
Keith
©2001 | Prentice Hall | Paper; 250 pp | Instock
ISBN-10: 0130418161 | ISBN-13: 9780130418166

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  Spence, Insel & Friedberg
  ©2008 | Prentice Hall | Electronic Book; 656 pp | Instock
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  Spence, Insel & Friedberg
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