Student Solutions Manual for Poole’s Linear Algebra: A Modern Introduction, 2nd

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  • Edition: 2nd
  • Format: Paperback
  • Copyright: 2005-07-22
  • Publisher: Brooks Cole
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Supplemental Materials

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  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.


By Robert Rogers of Bay State College. Provides detailed and complete solutions to the odd-numbered exercises and test questions; section and chapter summaries of symbols, definitions, and theorems; study tips and hints. Complex exercises are explored through a question-and-answer format designed to deepen understanding. Challenging and entertaining problems that further explore selected exercises are also included.

Table of Contents

Vectorsp. 1
The Geometry and Algebra of Vectorsp. 3
Length and Angle: The Dot Productp. 11
Exploration: Vectors and Geometryp. 25
Lines and Planesp. 27
Exploration: The Cross Productp. 45
Code Vectors and Modular Arithmeticp. 47
Chapter 1 Reviewp. 53
Systems of Linear Equationsp. 61
Introduction to Systems of Linear Equationsp. 63
Exploration: Lies My Computer Told Mep. 69
Direct Methods for Solving Linear Systemsp. 71
Exploration: Partial Pivotingp. 87
Exploration: An Introduction to the Analysis of Algorithmsp. 89
Spanning Sets and Linear Independencep. 91
Applicationsp. 109
Iterative Methods for Solving Linear Systemsp. 121
Chapter 2 Reviewp. 127
Matricesp. 135
Matrix Operationsp. 137
Matrix Algebrap. 143
The Inverse of a Matrixp. 155
The LU Factorizationp. 163
Subspaces, Basis, Dimension, and Rankp. 177
Introduction to Linear Transformationsp. 195
Applicationsp. 209
Chapter 3 Reviewp. 221
Eigenvalues and Eigenvectorsp. 231
Introduction to Eigenvalues and Eigenvectorsp. 233
Determinantsp. 247
Exploration: Geometric Applications of Determinantsp. 269
Eigenvalues and Eigenvectors of n x n Matricesp. 275
Similarity and Diagonalizationp. 287
Iterative Methods for Computing Eigenvaluesp. 299
Applications and the Perron-Frobenius Theoremp. 313
Chapter 4 Reviewp. 327
Orthogonalityp. 337
Orthogonality in Rnp. 339
Orthogonal Complements and Projectionsp. 349
The Gram-Schmidt Process and the QR Factorizationp. 355
Exploration: The Modified QR Factorizationp. 359
Exploration: Approximating Eigenvalues with the QR Algorithmp. 361
Orthogonal Diagonalization of Symmetric Matricesp. 363
Applicationsp. 369
Chapter 5 Reviewp. 381
Vector Spacesp. 395
Vector Spaces and Subspacesp. 397
Linear Independence, Basis, and Dimensionp. 403
Exploration: Magic Squaresp. 413
Change of Basisp. 415
Linear Transformationsp. 423
The Kernel and Range of a Linear Transformationp. 429
The Matrix of a Linear Transformationp. 439
Exploration: Tilings, Lattices, and Crystallographic Restrictionp. 449
Applicationsp. 451
Chapter 6 Reviewp. 457
Distance and Approximationp. 471
Inner Product Spacesp. 473
Exploration: Vectors and Matrices with Complex Entriesp. 481
Exploration: Geometric Inequalities and Optimization Problemsp. 485
Norms and Distance Functionsp. 489
Least Squares Approximationp. 497
The Singular Value Decompositionp. 505
Applicationsp. 515
Chapter 7 Reviewp. 521
Key Definitions and Conceptsp. 535
Theoremsp. 559
Table of Contents provided by Ingram. All Rights Reserved.

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