Title Linear Algebra with Applications, 9/e
Author Gareth Williams
ISBN 9789384323417
List price Rs 795.00
Price outside India Available on Request
Original price USD 164.95
Binding Paperback
No of pages 616
Book size 216 x 279 mm
Publishing year 2019
Original publisher Jones & Bartlett Learning
Published in India by Jones & Bartlett India Private Limited
Exclusive distributors Viva Books Private Limited
Sales territory India, Sri Lanka, Bangladesh, Pakistan, Nepal, .
Status New Arrival
About the book


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 Rn 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.


  • 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



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 Rn • Subspaces of Rn • 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


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.


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