# Elementary Linear Algebra (Classic Version) (2e)

##### Description

For a sophomore-level course in Linear Algebra

This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles.

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

##### Table of contents

**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 1 Review Exercises

Chapter 1 MATLAB Exercises

**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 2 Review Exercises

Chapter 2 MATLAB Exercises

**CHAPTER 3 DETERMINANTS** **192**

** 3.1 **Cofactor Expansion **192**

** 3.2 **Properties of Determinants **204**

Chapter 3 Review Exercises

Chapter 3 MATLAB Exercises

**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 4 Review Exercises

Chapter 4 MATLAB Exercises

**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 5 Review Exercises

Chapter 5 MATLAB Exercises

**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 *R*3 and Computer Graphics **452**

Chapter 6 Review Exercises

Chapter 6 MATLAB Exercises

**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**

Chapter 7 Review Exercises

Chapter 7 MATLAB Exercises

**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**

##### New to this edition

Significantly increased number of computation exercises

Complete redesign and development

##### Features & benefits

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.