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

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  • Edition: 3rd
  • Format: Paperback
  • Copyright: 2011-05-05
  • Publisher: Brooks Cole
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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.

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. 43
Applicationsp. 45
Reviewp. 51
Systems of Linear Equationsp. 59
Introduction to Systems of Linear Equationsp. 61
Exploration: Lies My Computer Told Mep. 67
Direct Methods for Solving Linear Systemsp. 69
Exploration: Partial Pivotingp. 85
Exploration: An Introduction to the Analysis of Algorithmsp. 87
Spanning Sets and Linear Independencep. 89
Applicationsp. 107
Iterative Methods for Solving Linear Systemsp. 119
Reviewp. 125
Matricesp. 133
Matrix Operations'p. 135
Matrix Algebrap. 141
The Inverse of a Matrixp. 153
The LU Factorizationp. 161
Subspaces, Basis, Dimension, and Rankp. 175
Introduction to Linear Transformationsp. 193
Applicationsp. 207
Reviewp. 223
Eigenvalues and Eigenvectorsp. 233
Introduction to Eigenvalues and Eigenvectorsp. 235
Determinantsp. 249
Exploration: Geometric Applications of Determinantsp. 271
Eigenvalues and Eigenvectors of n × n Matricesp. 277
Similarity and Diagonalizationp. 289
Iterative Methods for Computing Eigenvaluesp. 301
Applications and the Perron-Frobenius Theoremp. 315
Reviewp. 331
Orthogonalityp. 341
Orthogonality in Rnp. 343
Orthogonal Complements and Projectionsp. 353
The Gram-Schmidt Process and the QR Factorizationp. 359
Exploration: The Modified QR Factorizationp. 363
Exploration: Approximating Eigenvalues with the QR Algorithmp. 365
Orthogonal Diagonalization of Symmetric Matricesp. 367
Applicationsp. 373
Reviewp. 387
Vector Spacesp. 401
Vector Spaces and Subspacesp. 403
Linear Independence, Basis, and Dimensionp. 409
Exploration: Magic Squaresp. 419
Change of Basisp. 421
Linear Transformationsp. 429
The Kernel and Range of a Linear Transformationp. 435
The Matrix of a Linear Transformationp. 445
Exploration: Tilings, Lattices, and Crystallographic Restrictionp. 455
Applicationsp. 457
Distance and Approximationp. 477
Inner Product Spacesp. 479
Exploration: Vectors and Matrices with Complex Entriesp. 491
Norms and Distance Functionsp. 495
Least Squares Approximationp. 503
The Singular Value Decompositionp. 511
Applicationsp. 521
Reviewp. 527
Key Definitions and Conceptsp. 541
Theoremsp. 565
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