## Description

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.**CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.**

## 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**

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Elementary Linear Algebra, CourseSmart eTextbook, 2nd Edition

Format: Safari Book

$78.99 | ISBN-13: 978-0-13-605826-7