Skip to main content Skip to main navigation
  1. Home
  2. Computer Science & IT
  3. Advanced Math
  4. Linear Algebra
  5. Linear Algebra and its Applications


MyLab Math 18-Week Access Card to accompany Lay/Lay/McDonald, Linear Algebra and Its Applications, 6/e

This item is an access card for MyLab Math. This physical access card includes an access code for your MyLab Math course. In order to access the online course you will also need a Course ID, provided by your instructor.

This title-specific access card provides access to the Lay/Lay/McDonald, Linear Algebra and Its Applications 6/e accompanying MyLab course ONLY.


MyLab Math is the world’s leading online tutorial, and assessment program designed to help you learn and succeed in your mathematics course. MyLab Math online courses are created to accompany one of Pearson’s  best-selling math textbooks. Every MyLab Math course includes a complete, interactive eText.  Learn more about MyLab Math.


Before you purchase, check with your instructor or review your course syllabus to ensure that you select the correct ISBN.

Used or rental books

If you rent or purchase a used book with an access code, the access code may have been redeemed previously and you may have to purchase a new access code.


Access codes

Access codes that are purchased from sellers other than Pearson carry a higher risk of being either the wrong ISBN or a previously redeemed code. Check with the seller prior to purchase.

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


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 Input–Output Model

2.7 Applications to Computer Graphics

2.8 Subspaces of Rn

2.9 Dimension and Rank


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


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


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


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 Gram–Schmidt Process

6.5 Least-Squares Problems

6.6 Machine Learning and Linear Models

6.7 Inner Product Spaces

6.8 Applications of Inner Product Spaces


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


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


Supplementary Exercises


9. Optimization 

Introductory Example: The Berlin Airlift

9.1 Matrix Games

9.2 Linear Programming—Geometric Method

9.3 Linear Programming—Simplex Method

9.4 Duality


Supplementary Exercises


10. Finite-State Markov Chains (Online Only)

Introductory Example: Googling Markov Chains

10.1 Introduction and Examples

10.2 The Steady-State 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



A. Uniqueness of the Reduced Echelon Form

B. Complex Numbers

For teachers

All the material you need to teach your courses.

Discover teaching material