# Student Solutions Manual with Study Guide for Poole's Linear Algebra: A Modern Introduction, 3rd / Edition 3

ISBN-10: 0538737719

ISBN-13: 9780538737715

Pub. Date: 05/05/2011

Publisher: Cengage Learning

Contains detailed worked solutions to all odd-numbered exercises in the text; section and chapter summaries of symbols, definitions, and theorems; and study tips and hints. Complex exercises are explored through a question-and-answer format designed to deeper understanding. Challenging and entertaining problems that further explore selected exercises are also…  See more details below

## Overview

Contains detailed worked solutions to all odd-numbered exercises in the text; section and chapter summaries of symbols, definitions, and theorems; and study tips and hints. Complex exercises are explored through a question-and-answer format designed to deeper understanding. Challenging and entertaining problems that further explore selected exercises are also included.

## Product Details

ISBN-13:
9780538737715
Publisher:
Cengage Learning
Publication date:
05/05/2011
Edition description:
Solution M
Pages:
592
Product dimensions:
8.50(w) x 10.80(h) x 1.30(d)

1 Vectors 1

1.1 The Geometry and Algebra of Vectors 3

1.2 Length and Angle: The Dot Product 11

Exploration: Vectors and Geometry 25

1.3 Lines and Planes 27

Exploration: The Cross Product 43

1.4 Applications 45

Chapter 1 Review 51

2 Systems of Linear Equations 59

2.1 Introduction to Systems of Linear Equations 61

Exploration: Lies My Computer Told Me 67

2.2 Direct Methods for Solving Linear Systems 69

Exploration: Partial Pivoting 85

Exploration: An Introduction to the Analysis of Algorithms 87

2.3 Spanning Sets and Linear Independence 89

2.4 Applications 107

2.5 Iterative Methods for Solving Linear Systems 119

Chapter 2 Review 125

3 Matrices 133

3.1 Matrix Operations' 135

3.2 Matrix Algebra 141

3.3 The Inverse of a Matrix 153

3.4 The LU Factorization 161

3.5 Subspaces, Basis, Dimension, and Rank 175

3.6 Introduction to Linear Transformations 193

3.7 Applications 207

Chapter 3 Review 223

4 Eigenvalues and Eigenvectors 233

4.1 Introduction to Eigenvalues and Eigenvectors 235

4.2 Determinants 249

Exploration: Geometric Applications of Determinants 271

4.3 Eigenvalues and Eigenvectors of n × n Matrices 277

4.4 Similarity and Diagonalization 289

4.5 Iterative Methods for Computing Eigenvalues 301

4.6 Applications and the Perron-Frobenius Theorem 315

Chapter 4 Review 331

5 Orthogonality 341

5.1 Orthogonality in Rn 343

5.2 Orthogonal Complements and Projections 353

5.3 The Gram-Schmidt Process and the QR Factorization 359

Exploration: The Modified QR Factorization 363

Exploration: Approximating Eigenvalues with the QR Algorithm 365

5.4 Orthogonal Diagonalization of Symmetric Matrices 367

5.5 Applications 373

Chapter 5 Review 387

6 Vector Spaces 401

6.1 Vector Spaces and Subspaces 403

6.2 Linear Independence, Basis, and Dimension 409

Exploration: Magic Squares 419

6.3 Change of Basis 421

6.4 Linear Transformations 429

6.5 The Kernel and Range of a Linear Transformation 435

6.6 The Matrix of a Linear Transformation 445

Exploration: Tilings, Lattices, and Crystallographic Restriction 455

6.7 Applications 457

Chapter 6 Review463

7 Distance and Approximation 477

7.1 Inner Product Spaces 479

Exploration: Vectors and Matrices with Complex Entries 491

7.2 Norms and Distance Functions 495

7.3 Least Squares Approximation 503

7.4 The Singular Value Decomposition 511

7.5 Applications 521

Chapter 7 Review 527

Appendix I Key Definitions and Concepts 541

Appendix II Theorems 565