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

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  • Edition: 2nd
  • Format: Paperback
  • Copyright: 7/22/2005
  • Publisher: Brooks Cole
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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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