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# Elementary Linear Algebra, 7th Edition

## About

### Overview

The cornerstone of ELEMENTARY LINEAR ALGEBRA is the authors' clear, careful, and concise presentation of material--written so that readers can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. Featuring a new design that highlights the relevance of the mathematics and improves readability, the Seventh Edition also incorporates new conceptual Capstone exercises that reinforce multiple concepts in each section. Data and applications reflect current statistics and examples to engage users and demonstrate the link between theory and practice.

### Features and Benefits

• Coverage of Computer Algebra Systems (CAS) includes an online technology guide. Appendix B--also available online--offers an introduction to MATLAB, Maple, Mathematica, and Graphing Calculators; a walkthrough of the keystrokes needed for select examples; an applications section; and "Technology Pitfalls" students may encounter in using their CAS.
• All real data in the exercises and examples has been updated to reflect current statistics and information. Many new exercises have been added to the text as well.
• Learning objectives are available at the beginning of every section and online at the student website for quick reference and/or review.
• Guided Proofs help students successfully complete theoretical proofs by leading them, step-by-step, through the logical sequence of statements necessary to reach the correct conclusion.
• Pedagogical support--including self-assessment tools, review sections, and writing activities--allows students to check their understanding of each section and helps them develop critical thinking skills.

### Table of Contents

1. SYSTEMS OF LINEAR EQUATIONS
Introduction to Systems of Equations. Gaussian Elimination and Gauss-Jordan Elimination. Applications of Systems of Linear Equations.
2. MATRICES.
Operations with Matrices. Properties of Matrix Operations. The Inverse of a Matrix. Elementary Matrices. Applications of Matrix Operations.
3. DETERMINANTS.
The Determinant of a Matrix. Evaluation of a Determinant Using Elementary Operations. Properties of Determinants. Applications of Determinants.
4. VECTOR SPACES.
Vectors in Rn. Vector Spaces. Subspaces of Vector Spaces. Spanning Sets and Linear Independence. Basis and Dimension. Rank of a Matrix and Systems of Linear Equations. Coordinates and Change of Basis. Applications of Vector Spaces.
5. INNER PRODUCT SPACES.
Length and Dot Product in Rn. Inner Product Spaces. Orthogonal Bases: Gram-Schmidt Process. Mathematical Models and Least Squares Analysis. Applications of Inner Product Spaces.
6. LINEAR TRANSFORMATIONS.
Introduction to Linear Transformations. The Kernel and Range of a Linear Transformation. Matrices for Linear Transformations. Transition Matrices and Similarity. Applications of Linear Transformations.
7. EIGENVALUES AND EIGENVECTORS.
Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices and Orthogonal Diagonalization. Applications of Eigenvalues and Eigenvectors.
8. COMPLEX VECTOR SPACES (online).
Complex Numbers. Conjugates and Division of Complex Numbers. Polar Form and Demoivre's Theorem. Complex Vector Spaces and Inner Products. Unitary and Hermitian Spaces.
9. LINEAR PROGRAMMING (online).
Systems of Linear Inequalities. Linear Programming Involving Two Variables. The Simplex Method: Maximization. The Simplex Method: Minimization. The Simplex Method: Mixed Constraints.
10. NUMERICAL METHODS (online).
Gaussian Elimination with Partial Pivoting. Iterative Methods for Solving Linear Systems. Power Method for Approximating Eigenvalues. Applications of Numerical Methods.

### What's New

• Enhanced WebAssignÂ® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback and rich tutorial content to help them develop a deeper conceptual understanding of their subject matter. Students have access to an interactive eBook offering links to YouTube videos, video solutions, and more to bring the mathematics to life. You can build online assignments by selecting from thousands of text-specific problems, supplemented with problems from any Cengage Learning textbook.
• A new, more student-friendly design includes a greater number of images that make content more relevant for students. The trim size and font size in the exercise sets have been increased, making the text easier for students to read.
• To motivate students by emphasizing the relevance of the content, each chapter opener contains a list of sections, five photos with references to applications, and an arrow indicating the section in which each application appears.
• New Capstone exercises, each of which covers several concepts, have been added in each section. Conceptual in nature, they reinforce key ideas learned in the section without being time-consuming or tedious for students.

### Learning Resource Bundles

Choose the textbook packaged with the resources that best meet your course and student needs. Contact your Learning Consultant for more information.

### Bundle: Text + Enhanced WebAssign Printed Access Card for Applied Math, Single-Term Courses

ISBN-10: 113342659X  | ISBN-13: 9781133426592

List Price = \$351.95

### Bundle: Text + Student Solutions Manual

ISBN-10:  113380408X  | ISBN-13:  9781133804086

List Price = \$446.95  | CengageBrain Price = \$446.95

### ePack: Printed Text + Enhanced WebAssign for Advanced Math, 1 term (6 months) Instant Access

ISBN-10:  128593928X  | ISBN-13:  9781285939285

List Price = \$351.95  | CengageBrain Price = \$351.95

### Printed Text + Enhanced WebAssign Instant Access for Applied Math, Single-Term Courses

ISBN-10:  1305593227 | ISBN-13:  9781305593220

List Price = \$351.95  | CengageBrain Price = \$351.95

## Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

### Instructor Supplements

#### Solution Builder  (ISBN-10: 1133489575 | ISBN-13: 9781133489573)

This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. www.cengage.com/solutionbuilder

#### Student Solutions Manual  (ISBN-10: 1133111327 | ISBN-13: 9781133111320)

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

List Price = \$101.95  | CengageBrain Price = \$101.95  | College Bookstore Wholesale Price = \$76.50

#### Enhanced WebAssign - Start Smart Guide for Students  (ISBN-10: 0495384798 | ISBN-13: 9780495384793)

If your instructor has chosen to package Enhanced WebAssign with your text, this manual will help you get up and running quickly with the Enhanced WebAssign system so you can study smarter and improve your performance in class.

List Price = \$49.95  | CengageBrain Price = \$49.95  | College Bookstore Wholesale Price = \$37.50

#### Enhanced WebAssign Instant Access for Advanced Math, Single-Term Courses  (ISBN-10: 1285858271 | ISBN-13: 9781285858272)

IMPORTANT: When purchasing this instant access code for Advanced Math, ensure that you are using it in one of the following courses: Differential Equations or Linear Algebra. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = \$94.00  | CengageBrain Price = \$94.00  | College Bookstore Wholesale Price = \$94.00

### Student Supplements

#### Student Solutions Manual  (ISBN-10: 1133111327 | ISBN-13: 9781133111320)

Go beyond the answers--see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text, giving you the information you need to truly understand how these problems are solved.

List Price = \$101.95  | CengageBrain Price = \$101.95  | College Bookstore Wholesale Price = \$76.50

#### Enhanced WebAssign - Start Smart Guide for Students  (ISBN-10: 0495384798 | ISBN-13: 9780495384793)

If your instructor has chosen to package Enhanced WebAssign with your text, this manual will help you get up and running quickly with the Enhanced WebAssign system so you can study smarter and improve your performance in class.

List Price = \$49.95  | CengageBrain Price = \$49.95  | College Bookstore Wholesale Price = \$37.50

#### Enhanced WebAssign Instant Access for Advanced Math, Single-Term Courses  (ISBN-10: 1285858271 | ISBN-13: 9781285858272)

IMPORTANT: When purchasing this instant access code for Advanced Math, ensure that you are using it in one of the following courses: Differential Equations or Linear Algebra. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = \$94.00  | CengageBrain Price = \$94.00  | College Bookstore Wholesale Price = \$94.00

## Meet the Author

### Ron Larson

Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2014 Text and Academic Authors Association TEXTY Award for PRECALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning.