Student Solutions Manual to accompany Elementary Linear Algebra, Applications version, 11e

CHAPTER 1: SYSTEMS OF LINEAR EQUATIONS AND MATRICES

1.1 Introduction to Systems of Linear Equations

1.2 Gaussian Elimination

1.3 Matrices and Matrix Operations

1.4 Inverses; Algebraic Properties of Matrices

1.5 Elementary Matrices and a Method for Finding A-1

1.6 More on Linear Systems and Invertible Matrices

1.7 Diagonal, Triangular, and Symmetric Matrices

1.8 Matrix Transformations

1.9 Applications of Linear Systems

1.10 Leontief Input-Output Models

Chapter 1 Supplementary Exercises

CHAPTER 2: DETERMINANTS

2.1 Determinants by Cofactor Expansion

2.2 Evaluating Determinants by Row Reduction

2.3 Properties of Determinants; Cramer's Rule

Chapter 2 Supplementary Exercises

CHAPTER 3: EUCLIDEAN VECTOR SPACES

3.1 Vectors in 2-Space, 3-Space, and n-Space

3.2 Norm, Dot Product, and Distance in Rn

3.3 Orthogonality

3.4 The Geometry of Linear Systems

3.5 Cross Product

Chapter 3 Supplementary Exercises

CHAPTER 4: GENERAL VECTOR SPACES

4.1 Real Vector Spaces

4.2 Subspaces

4.3 Linear Independence

4.4 Coordinates and Basis

4.5 Dimension

4.6 Change of Basis

4.7 Row Space, Column Space, and Null Space

4.8 Rank, Nullity, and the Fundamental Matrix Spaces

4.9 Matrix Transformations from Rn to Rm

4.10 Properties of Matrix Transformations

4.11 Geometry of Matrix Operators on R2

Chapter 4 Supplementary Exercises

CHAPTER 5: EIGENVALUES AND EIGENVECTORS

5.1 Eigenvalues and Eigenvectors

5.2 Diagonalization

5.3 Complex Vector Spaces

5.4 Differential Equations

5.5 Dynamical Systems and Markov Chains

Chapter 5 Supplementary Exercises

CHAPTER 6: INNER PRODUCT SPACES

6.1 Inner Products

6.2 Angle and Orthogonality in Inner Product Spaces

6.3 Gram-Schmidt Process; QR-Decomposition

6.4 Best Approximation; Least Squares

6.5 Mathematical Modeling Using Least Squares

6.6 Function Approximation; Fourier Series

Chapter 6 Supplementary Exercises

CHAPTER 7: DIAGONALIZATION AND QUADRATIC FORMS

7.1 Orthogonal Matrices

7.2 Orthogonal Diagonalization

7.3 Quadratic Forms

7.4 Optimization Using Quadratic Forms

7.5 Hermitian, Unitary, and Normal Matrices

Chapter 7 Supplementary Exercises

CHAPTER 8: LINEAR TRANSFORMATIONS

8.1 General Linear Transformations

8.2 Compositions and Inverse Transformations

8.3 Isomorphism

8.4 Matrices for General Linear Transformations

8.5 Similarity

Chapter 8 Supplementary Exercises

CHAPTER 9: NUMERICAL METHODS

9.1 LU-Decompositions

9.2 The Power Method

9.3 Comparison of Procedures for Solving Linear Systems

9.4 Singular Value Decomposition

9.5 Data Compression Using Singular Value Decomposition

Chapter 9 Supplementary Exercises

CHAPTER 10: APPLICATIONS OF LINEAR ALGEBRA

10.1 Constructing Curves and Surfaces Through Specified Points

10.2 The Earliest Applications of Linear Algebra

10.3 Cubic Spline Interpolation

10.4 Markov Chains

10.5 Graph Theory

10.6 Games of Strategy

10.7 Leontief Economic Models

10.8 Forest Management

10.9 Computer Graphics

10.10 Equilibrium Temperature Distributions

10.11 Computed Tomography

10.12 Fractals

10.13 Chaos

10.14 Cryptography

10.15 Genetics

10.16 Age-Specific Population Growth

10.17 Harvesting of Animal Populations

10.18 A Least Squares Model for Human Hearing

10.19 Warps and Morphs

10.20 Internet Search Engines