**Description:**

**Linear Algebra with Applications, Ninth
Edition** is designed for the introductory course in linear
algebra for students within engineering, mathematics, business management, and
physics. Updated to increase clarity and improve student learning, the author
provides a flexible blend of theory and engaging applications.

The material in **Linear Algebra with Applications,
Ninth Edition** is arranged into three parts that contain core and optional
sections:

Part 1
introduces the basics, discussing systems of linear equations, vectors in **R**^{n} matrices, linear
transformations, determinants, eigenvalues, and eigenspaces.

Part 2
builds on this material to discuss general vector spaces, and includes such
topics as the rank/nullity theorem, inner products, and coordinate
representation.

Part 3
completes the course with important ideas and methods in numerical linear
algebra including ill-conditioning, pivoting, LU decomposition, and singular
value decomposition.

Throughout the text the author provides interesting
applications, ranging from theoretical applications such as the use of linear
algebra in differential equations, to many practical applications in the fields
of electrical engineering, traffic analysis, relativity, history, and more.

**KEY FEATURES OF THE ****NINTH
EDITION**

- NEW
simple-to-advanced organizational framework
- Interesting
applications, both theoretical and practical, engage and challenge students
- Carefully
explained and illustrated examples highlights key concepts throughout the text
- A
MATLAB manual, included as an appendix, consists of 31 sections that tie into
course material
- Available
with WebAssign Online Homework and Assessment with integrated eBook

**Contents: **

**Preface**

__Part
1: Linear Equations, Vectors, and Matrices__

**Chapter 1: Linear Equations
and Vectors** • Matrices and Systems of Linear Equations •
Gauss-Jordan Elimination • The Vector Space **R**^{n} •
Subspaces of **R**^{n} •
Basis and Dimension • Dot Product, Norm, Angle, and Distance (Option: This
section can be deferred to just before Section 4.6.) • Curve Fitting,
Electrical Networks, and Traffic Flow • Chapter 1 Review Exercises

**Chapter 2: Matrices and
Linear Transformations** • Addition, Scalar Multiplication, and
Multiplication of Matrices • Properties of Matrix Operations • Symmetric
Matrices and Seriation in Archaeology • The Inverse of a Matrix and
Cryptography • Matrix Transformations, Rotations, and Dilations • Linear
Transformations, Graphics, and Fractals • The Leontief Input-Output Model in
Economics • Markov Chains, Population Movements, and Genetics • A Communication
Model and Group Relationships in Sociology • Chapter 2 Review Exercises

**Chapter 3: Determinants and
Eigenvectors** • Introduction to Determinants • Properties
of Determinants • Determinants, Matrix Inverses, and Systems of Linear
Equations • Eigenvalues and Eigenvectors (Option: Diagonalization of Matrices,
Section 5.3, may be discussed at this time.) • Google, Demography, Weather
Prediction, and Leslie Matrix Models • Chapter 3 Review Exercises

__Part
2: Vector Spaces__

**Chapter 4: General Vector
Spaces** • General Vector Spaces and Subspaces • Linear
Combinations of Vectors • Linear Independence of Vectors • Properties of Bases
• Rank • Projections, Gram-Schmidt Process, and QR Factorization • Orthogonal
Complement • Kernel, Range, and the Rank/Nullity Theorem • One-to-One
Transformations and Inverse Transformations • Transformations and Systems of
Linear Equations • Chapter 4 Review Exercises

**Chapter 5: Coordinate
Representations** • Coordinate Vectors • Matrix
Representations of Linear Transformations • Diagonalization of Matrices •
Quadratic Forms, Difference Equations, and Normal Modes • Linear Differential
Equations (Calculus Prerequisite) • Chapter 5 Review Exercises

**Chapter 6: Inner Product
Spaces** • Inner Product Spaces • Non-Euclidean Geometry and
Special Relativity • Approximation of Functions and Coding Theory • Least
Squares Solutions • Chapter 6 Review Exercises

__Part
3: Numerical Linear Algebra__

**Chapter 7: Numerical
Methods** • Gaussian Elimination • The Method of LU Decomposition
• Practical Difficulties in Solving Systems of Equations • Iterative Methods
for Solving Systems of Linear Equations • Eigenvalues by Iteration and
Connectivity of Networks • The Singular Value Decomposition • Chapter 7 Review
Exercises

**Chapter 8: Linear
Programming** • A Geometrical Introduction to Linear Programming • The
Simplex Method • Geometrical Explanation of the Simplex Method • Chapter 8
Review Exercises

**Appendices** •
Cross Product • Equations of Planes and Lines in Three-Space • Graphing
Calculator Manual • Reduced Echelon Form of a Matrix • Matrix Operations •
Powers of a Matrix • Transpose of a Matrix • Inverse of a Matrix • Determinant
of a Matrix • Summary of Formats for Row Operations • MATLAB Manual • Entering
and Displaying a Matrix (Section 1.1) • Solving Systems of Linear Equations
(Sections 1.1, 1.2, 1.7) • Dot Product, Norm, Angle, Distance (Section 1.6) •
Matrix Operations (Sections 2.1-2.3) • Computational Considerations (Section
2.2) • Inverse of a Matrix (Section 2.4) • Solving Systems of Equations Using
Matrix Inverse (Section 2.4) • Cryptography (Section 2.4) • Transformations
Defined by Matrices (Sections 2.5, 2.6) • Fractals (Section 2.6) • Leontief I/O
Model (Section 2.7) • Markov Chains (Sections 2.8, 3.5) • Digraphs (Section
2.9) • Determinants (Sections 3.1-3.3) • Cramer’s Rule (Section 3.3) •
Eigenvalues and Eigenvectors (Sections 3.4, 3.5) • Linear Combinations,
Dependence, Basis, Rank (Sections 1.3, 4.2-4.5) • Projection, Gram-Schmidt
Orthogonalization (Section 4.6) • QR Factorization (Section 4.6) • Kernel and
Range (Section 4.8) • Inner Product, Non-Euclidean Geometry (Sections 6.1, 6 2)
• Space-Time Travel (Section 6.2) • Pseudoinverse and Least Squares Curves
(Section 6.4) • LU Decomposition (Section 7.2) • Condition Number of a Matrix
(Section 7.3) • Jacobi and Gauss-Seidel Iterative Methods (Section 7.4) •
Singular Value Decomposition (Section 7.6) • The Simplex Method in Linear Programming
(Section 8.2) • Cross Product (Appendix A) • MATLAB Commands, Functions, and
M-Files • The Linear Algebra with Applications Toolbox M-Files

**Answers to Selected
Exercises**

**Index**

**About the Author: **

**Gareth Williams - Stetson University**

Gareth Williams earned a B.S. and a
Ph.D. in applied mathematics from the University of Wales, and did graduate
work at Kings College University of London. He has taught mathematics at the
University of Florida, the University of Denver, and Stetson University. He has
been an exchange professor at the Paedagogische Hochschule, in Freiburg,
Germany and has spent sabbaticals at the University of Wales. His mathematical
interests include linear algebra, relativity, mathematical modeling, and the
computer in mathematics education.

His
publications include “Fine Topologies for Minkowski Space”, “Motions in
Relativistic Space”, “Mathematics in Archaeology”, and books on Finite
Mathematics, Calculus, and College Algebra. He is the co-developer (with Lisa
Coulter) of the linear algebra software package, “The Linear Algebra Toolbox”
for MATLAB.

Dr. Williams is a member of The Mathematics Association of America.

**Target
Audience:**

This book is
helpful for the students and academicians of Mathematics.