# Pearson eText for Linear Algebra with Applications -- Access Card, 10th edition

Published by Pearson (June 5th 2019) - Copyright © 2020

10th edition

ISBN-13: 9780135261705

### What's included

## Overview

NOTE: This loose-leaf, three-hole punched version of the textbook gives you the flexibility to take only what you need to class and add your own notes – all at an affordable price.

*For sophomore-level or junior/senior-level first courses in linear algebra; assumes calculus as a prerequisite.*

**A thorough and accessible introduction to linear algebra, delivered digitally**

The new **10th Edition of Linear Algebra with Applications** continues to encourage a challenging and broad understanding of the subject. For this edition, Steve Leon — one of the leading figures in the use of technology for linear algebra — is joined by new co-author Lisette de Pillis of Harvey Mudd College, who brings her passion for teaching and solving real-world problems to this revision.

Key to the **10th Edition** was transforming from a primarily print-based resource to a digital learning tool. The eText is packed with content and tools, such as interactive figures, that help bring course content to life for students and augment instruction. This change in format supports the authors’ hallmark — using modern practical application to make key concepts tangible and demonstrating how mathematics is used in the real world.

Each chapter contains integrated worked examples, practical applications, computer exercises, and chapter tests. The important roles played by geometry and visualization in understanding linear algebra are emphasized.

## Table of contents

**1. Matrices and Systems of Equations **

1.1 Systems of Linear Equations

1.2 Row Echelon Form

1.3 Matrix Arithmetic

1.4 Matrix Algebra

1.5 Elementary Matrices

1.6 Partitioned Matrices

MATLAB Exercises

Chapter Test A — True or False

Chapter Test B

**2. Determinants**

2.1 The Determinant of a Matrix

2.2 Properties of Determinants

2.3 Additional Topics and Applications

MATLAB Exercises

Chapter Test A — True or False

Chapter Test B

**3. Vector Spaces**

3.1 Definition and Examples

3.2 Subspaces

3.3 Linear Independence

3.4 Basis and Dimension

3.5 Change of Basis

3.6 Row Space and Column Space

MATLAB Exercises

Chapter Test A — True or False

Chapter Test B

**4. Linear Transformations**

4.1 Definition and Examples

4.2 Matrix Representations of Linear Transformations

4.3 Similarity

MATLAB Exercises

Chapter Test A — True or False

Chapter Test B

**5. Orthogonality**

5.1 The Scalar Product in R^{n}

5.2 Orthogonal Subspaces

5.3 Least Squares Problems

5.4 Inner Product Spaces

5.5 Orthonormal Sets

5.6 The Gram–Schmidt Orthogonalization Process

5.7 Orthogonal Polynomials

MATLAB Exercises

Chapter Test A — True or False

Chapter Test B

**6. Eigenvalues**

6.1 Eigenvalues and Eigenvectors

6.2 Systems of Linear Differential Equations

6.3 Diagonalization

6.4 Hermitian Matrices

6.5 The Singular Value Decomposition

6.6 Quadratic Forms

6.7 Positive Definite Matrices

6.8 Nonnegative Matrices

MATLAB Exercises

Chapter Test A — True or False

Chapter Test B

**7. Numerical Linear Algebra**

7.1 Floating-Point Numbers

7.2 Gaussian Elimination

7.3 Pivoting Strategies

7.4 Matrix Norms and Condition Numbers

7.5 Orthogonal Transformations

7.6 The Eigenvalue Problem

7.7 Least Squares Problems

7.8 Iterative Methods

MATLAB Exercises

Chapter Test A — True or False

Chapter Test B

**8. Canonical Forms**

8.1 Nilpotent Operators

8.2 The Jordan Canonical Form

**Appendix: MATLAB**

**Bibliography**

**Answers to Selected Exercises**

**Index**

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