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

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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.

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Product Details

  • ISBN-13: 9780538737715
  • Publisher: Cengage Learning
  • Publication date: 5/5/2011
  • Edition description: Solution M
  • Edition number: 3
  • Pages: 592
  • Product dimensions: 8.50 (w) x 10.80 (h) x 1.30 (d)

Meet the Author

David Poole is Professor of Mathematics at Trent University, where he has been a faculty member since 1984. Dr. Poole has won numerous teaching awards: Trent University's Symons Award for Excellence in Teaching (the university's top teaching award), three merit awards for teaching excellence, a 2002 Ontario Confederation of University Faculty Associations Teaching Award (the top university teaching award in the province), a 2003 3M Teaching Fellowship (the top university teaching award in Canada, sponsored by 3M Canada Ltd.), a 2007 Leadership in Faculty Teaching Award from the province of Ontario, and the Canadian Mathematical Society's 2009 Excellence in Teaching Award. From 2002-2007, Dr. Poole was Trent University's Associate Dean (Teaching & Learning). His research interests include discrete mathematics, ring theory, and mathematics education. He received his B.Sc. from Acadia University in 1976 before earning his M.Sc. (1977) and Ph.D. (1984) from McMaster University. When he is not doing mathematics, David Poole enjoys hiking and cooking, and he is an avid film buff.

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Table of Contents

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

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