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Linear Algebra with Applications

by Williams, Gareth

ISBN13: 9780763732356
ISBN10: 0763732354
Additional ISBN(s): 9780763757533
Edition: 5th
Format: Hardcover
Copyright: 2004-09-01
Publisher: Jones & Bartlett
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1. Linear Algebra with Applications > ISBN13: 9780763732356

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Summary

Linear Algebra with Applications, Fifth Edition is designed for an introductory course in linear algebra.

Systems of Linear Equations

(42)

Matrices and Systems of Linear Equations

(14)

Gauss-Jordan Elimination

(12)

Curve Fitting, Electrical Networks, and Traffic Flow

(15)

Chapter 1 Review Exercises

(4)

Matrices

(88)

Addition, Scalar Multiplication, and Multiplication of Matrices

(17)

Algebraic Properties of Matrix Operations

(13)

Symmetric Matrices and Seriation in Archaeology

(12)

The Inverse of a Matrix and Cryptography

(16)

The Leontief Input-Output Model in Economics

102

(6)

Markov Chains, Population Movements, and Genetics

108

(9)

A Communication Model and Group Relationships in Sociology

117

(14)

Chapter 2 Review Exercises

128

(3)

Determinants

131

(36)

Introduction to Determinants

132

(9)

Properties of Determinants

141

(7)

Numerical Evaluation of a Determinant

148

(5)

Determinants, Matrix Inverses, and Systems of Linear Equations

153

(14)

Chapter 3 Review Exercises

161

(6)

Vector Spaces

167

(104)

The Vector Space Rn

168

(10)

Dot Product, Norm, Angle, and Distance

178

(15)

General Vector Spaces

193

(7)

Subspaces

200

(7)

Linear Combinations of Vectors

207

(14)

Linear Dependence and Independence

221

(7)

Basis and Dimension

228

(11)

Rank of a Matrix

239

(12)

Orthonormal Vectors and Projections in Rn

251

(20)

Chapter 4 Review Exercises

265

(6)

Eigenvalues and Eigenvectors

271

(42)

Eigenvalues and Eigenvectors

272

(7)

Demography and Weather Prediction

279

(7)

Diagonalization of Matrices

286

(11)

Quadratic Forms, Difference Equations, and Normal Modes

297

(16)

Chapter 5 Review Exercises

312

(1)

Linear Transformations

313

(78)

Introduction to Linear Transformations

314

(9)

Matrix Transformations, Computer Graphics, and Fractals

323

(21)

Kernel and Range

344

(12)

Transformations and Systems of Linear Equations

356

(9)

Coordinate Vectors

365

(10)

Matrix Representations of Linear Transformations

375

(16)

Chapter 6 Review Exercises

388

(3)

Inner Product Spaces

391

(40)

Inner Product Spaces

392

(10)

Non-Euclidean Geometry and Special Relativity

402

(7)

Approximation of Functions and Coding Theory

409

(8)

Least-Squares Curves

417

(14)

Chapter 7 Review Exercises

430

(1)

Numerical Techniques

431

(46)

Gaussian Elimination

432

(6)

The Method of LU Decomposition

438

(8)

Practical Difficulties in Solving systems of Equations

446

(11)

Iterative Methods for Solving Systems of Linear Equations

457

(6)

Eigenvalues by Iteration; Connectivity of Networks

463

(14)

Chapter 8 Review Exercises

475

(2)

Linear Programming

477

(26)

A Geometrical Introduction to Linear Programming

478

(9)

The Simplex Method

487

(7)

Geometrical Explanation of the Simplex Method

494

(9)

Chapter 9 Review Exercises

501

(2)

Appendix A Cross Product

503

(12)

Appendix B Equations of Planes and Lines in Three-Space

515

(8)

Appendix C Graphing Calculator Manual

523

(6)

C.1 Reduced Echelon Form of a Matrix (Sections 1.1, 1.2)

524

(1)

C.2 Matrix Operations (Sections 2.1, 2.2)

524

(1)

C.3 Powers of a Matrix (Section 2.2)

525

(1)

C.4 Transpose of a Matrix (Section 2.3)

525

(1)

C.5 Inverse of a Matrix (Section 2.4)

526

(1)

C.6 Determinant of a Matrix (Section 3.1)

526

(1)

C.7 Summary of Formats for Row Operations (Sections 1.1, 1.2)

527

(2)

Appendix D MATLAB Manual

529

(62)

D.1 Entering and Displaying a Matrix (Section 1.1)

530

(1)

D.2 Solving Systems of Linear Equations (Sections 1.1, 1.2, 1.3)

531

(4)

D.3 Matrix Operations, Submatrices, Rows and Columns (Sections 2.1, 2.2, 2.3)

535

(1)

D.4 Matrix Operations (Sections 2.1, 2.2, 2.3)

535

(4)

D.5 Computational Considerations (Section 2.2)

539

(1)

D.6 Inverse of a Matrix (Section 2.4)

540

(2)

D.7 Solving Systems of Equations Using Matrix Inverse (Section 2.4)

542

(3)

D.8 Cryptography (Section 2.4)

545

(1)

D.9 Leontief I/O Model (Section 2.5)

546

(2)

D.10 Markov Chains (Sections 2.6, 6.2)

548

(3)

D.11 Digraphs (Section 2.7)

551

(2)

D.12 Determinants (Sections 3.1, 3.2, 3.3)

553

(1)

D.13 Cramer's Rule (Section 3.4)

554

(3)

D.14 Linear Combinations, Linear Dependence, Basis (Sections 4.5-4.7)

557

(2)

D.15 Projection, Gram-Schmidt Orthogonalization (Section 4.8)

559

(5)

D.16 Eigenvalues and Eigenvectors and Applications (Sections 5.1-5.4)

564

(1)

D.17 Transformations Defined by Matrices (Sections 6.1, 6.2)

564

(1)

D.18 Fractals (Section 6.2)

565

(3)

D.19 Kernel and Range (Section 6.3)

568

(1)

D.20 Inner Product, Non-Euclidean Geometry (Sections 7.1, 7.2)

569

(3)

D.21 Space-Time Travel (Section 7.2)

572

(2)

D.22 Pseudoinverse and Least-Squares Curves (Section 7.4)

574

(4)

D.23 LU Decomposition (Section 8.2)

578

(3)

D.24 Condition Number of a Matrix (Section 8.3)

581

(2)

D.25 Jacobi and Gauss-Seidel Iterative Methods (Section 8.4)

583

(3)

D.26 The Simplex Method in Linear Programming (Section 9.2)

D.27 Cross Product (Appendix A)

586

(2)

D.28 MATLAB Commands, Functions, and M-files

588

(1)

D.29 Linear Algebra with Applications Toolbox M-files

588

(3)

Answers to Selected Exercises

591

(66)

Index

657

Supplemental Materials

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Rent More, Save More! Use code: ECRENTAL

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5% off 1 book, 7% off 2 books, 10% off 3+ books

Linear Algebra with Applications

Summary

Table of Contents

Supplemental Materials

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