Linear Algebra and its Applications, 6th edition
Choose the option that's right for you
Single
$9.99 / mo
4month minimum term for $39.96
 Access this eText title
 Up to 2 devices
Multi
$14.99 / mo
4month minimum term for $59.96
 Access over 1,500 titles
 Up to 2 devices
 Discounted tutor access
Learn more, spend less

Study smarter, not harder
Save time with study tools in your eText

Watch and learn
Videos & animations bring concepts to life

Listen on the go
Learn how you like with full eText audio

Learn anytime, anywhere
Get the app to access your eText whenever you need it

Make it your own
Your notes. Your highlights. Your eText
Overview
Linear Algebra and Its Applications fosters the concepts and skills you'll use in your future career through a modern introduction with broad, relevant applications. With traditional texts, the early stages of the course are relatively easy as material is presented in a familiar, concrete setting, but abstract concepts become a problem. Certain concepts fundamental to the study of linear algebra (such as linear independence, vector space, and linear transformations) require time to assimilate  and your understanding of them is vital.
Lay, Lay, and McDonald make these concepts more accessible by introducing them early in a familiar, concrete R^{n} setting, developing them gradually, and returning to them throughout the text so that you can grasp them when they are discussed in the abstract. The 6th Edition offers exciting new material, examples, and online resources, along with new topics, vignettes, and applications.
Published by Pearson (July 10th 2020)  Copyright © 2021
ISBN13: 9780136880929
Subject: Advanced Math
Category: Linear Algebra
Table of contents
1. Linear Equations in Linear Algebra
Introductory Example: Linear Models in Economics and Engineering
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax = b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models in Business, Science, and Engineering
Projects
Supplementary Exercises
2. Matrix Algebra
Introductory Example: Computer Models in Aircraft Design
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices
2.5 Matrix Factorizations
2.6 The Leontief InputOutput Model
2.7 Applications to Computer Graphics
2.8 Subspaces of Rn
2.9 Dimension and Rank
Projects
Supplementary Exercises
3. Determinants
Introductory Example: Random Paths and Distortion
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume, and Linear Transformations
Projects
Supplementary Exercises
4. Vector Spaces
Introductory Example: Space Flight and Control Systems
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Change of Basis
4.7 Digital Signal Processing
4.8 Applications to Difference Equations
Projects
Supplementary Exercises
5. Eigenvalues and Eigenvectors
Introductory Example: Dynamical Systems and Spotted Owls
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
5.5 Complex Eigenvalues
5.6 Discrete Dynamical Systems
5.7 Applications to Differential Equations
5.8 Iterative Estimates for Eigenvalues
5.9 Markov Chains
Projects
Supplementary Exercises
6. Orthogonality and Least Squares
Introductory Example: The North American Datum and GPS Navigation
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The GramSchmidt Process
6.5 LeastSquares Problems
6.6 Machine Learning and Linear Models
6.7 Inner Product Spaces
6.8 Applications of Inner Product Spaces
Projects
Supplementary Exercises
7. Symmetric Matrices and Quadratic Forms
Introductory Example: Multichannel Image Processing
7.1 Diagonalization of Symmetric Matrices
7.2 Quadratic Forms
7.3 Constrained Optimization
7.4 The Singular Value Decomposition
7.5 Applications to Image Processing and Statistics
Projects
Supplementary Exercises
8. The Geometry of Vector Spaces
Introductory Example: The Platonic Solids
8.1 Affine Combinations
8.2 Affine Independence
8.3 Convex Combinations
8.4 Hyperplanes
8.5 Polytopes
8.6 Curves and Surfaces
Projects
Supplementary Exercises
9. Optimization
Introductory Example: The Berlin Airlift
9.1 Matrix Games
9.2 Linear ProgrammingGeometric Method
9.3 Linear ProgrammingSimplex Method
9.4 Duality
Projects
Supplementary Exercises
10. FiniteState Markov Chains (Online Only)
Introductory Example: Googling Markov Chains
10.1 Introduction and Examples
10.2 The SteadyState Vector and Google's PageRank
10.3 Communication Classes
10.4 Classification of States and Periodicity
10.5 The Fundamental Matrix
10.6 Markov Chains and Baseball Statistics
Appendices
A. Uniqueness of the Reduced Echelon Form
B. Complex Numbers
Your questions answered
Introducing Pearson+. Reimagined learning, designed for you. Choose from one eText or over 1,500 eTexts and study tools, all in one place, for one low monthly subscription. A new way to buy books that fits your budget. Make the most of your study time with offline access, enhanced search, notes and flashcards — to get organized, get the work done quicker and get results. Plus, with the app, put textbooks in your pocket and learn wherever. It's time to upgrade the textbook and simplify learning, so you can have time to live too.
Pearson eText is an easytouse digital textbook available from Pearson+. Make it your own by adding notes and highlights. Download the Pearson+ mobile app to learn on the go, even offline. Listen on the go with our new audiobook feature, available for most titles.
When you choose a plan, you're signing up for a 4month term. We will charge your payment method each month until your 4month term has ended. After that, we'll automatically renew your subscription and charge you on a monthtomonth basis unless you turn off autorenewal in My account.
When you purchase a Pearson+ subscription, it will last a minimum of 4 months, and then automatically renew each month thereafter unless you turn off autorenew in My account.
If you want to stop your subscription at the end of your 4month term, simply turn off autorenew from My account. To avoid the next payment charge, make sure you turn auto renewal off 1 day before the auto renewal date.
You can subscribe again after autorenew has been turned off by purchasing another Pearson+ subscription.
We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details before your first monthly payment.
With a Multi Pearson+ subscription plan, you can download up to 5 titles on the Pearson+ app from My list on each of your authorized devices every month.
When you're using your Multi Pearson+ subscription plan in a browser, you can select and read from as many titles as you like.