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

by Poole, David

• ISBN13: 9780538737715
• ISBN10: 0538737719
• Edition: 3rd
• Format: Paperback
• Copyright: 2011-05-05
• Publisher: Brooks Cole

Summary

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

Vectors	p. 1
The Geometry and Algebra of Vectors	p. 3
Length and Angle: The Dot Product	p. 11
Exploration: Vectors and Geometry	p. 25
Lines and Planes	p. 27
Exploration: The Cross Product	p. 43
Applications	p. 45
Review	p. 51
Systems of Linear Equations	p. 59
Introduction to Systems of Linear Equations	p. 61
Exploration: Lies My Computer Told Me	p. 67
Direct Methods for Solving Linear Systems	p. 69
Exploration: Partial Pivoting	p. 85
Exploration: An Introduction to the Analysis of Algorithms	p. 87
Spanning Sets and Linear Independence	p. 89
Applications	p. 107
Iterative Methods for Solving Linear Systems	p. 119
Review	p. 125
Matrices	p. 133
Matrix Operations'	p. 135
Matrix Algebra	p. 141
The Inverse of a Matrix	p. 153
The LU Factorization	p. 161
Subspaces, Basis, Dimension, and Rank	p. 175
Introduction to Linear Transformations	p. 193
Applications	p. 207
Review	p. 223
Eigenvalues and Eigenvectors	p. 233
Introduction to Eigenvalues and Eigenvectors	p. 235
Determinants	p. 249
Exploration: Geometric Applications of Determinants	p. 271
Eigenvalues and Eigenvectors of n × n Matrices	p. 277
Similarity and Diagonalization	p. 289
Iterative Methods for Computing Eigenvalues	p. 301
Applications and the Perron-Frobenius Theorem	p. 315
Review	p. 331
Orthogonality	p. 341
Orthogonality in Rn	p. 343
Orthogonal Complements and Projections	p. 353
The Gram-Schmidt Process and the QR Factorization	p. 359
Exploration: The Modified QR Factorization	p. 363
Exploration: Approximating Eigenvalues with the QR Algorithm	p. 365
Orthogonal Diagonalization of Symmetric Matrices	p. 367
Applications	p. 373
Review	p. 387
Vector Spaces	p. 401
Vector Spaces and Subspaces	p. 403
Linear Independence, Basis, and Dimension	p. 409
Exploration: Magic Squares	p. 419
Change of Basis	p. 421
Linear Transformations	p. 429
The Kernel and Range of a Linear Transformation	p. 435
The Matrix of a Linear Transformation	p. 445
Exploration: Tilings, Lattices, and Crystallographic Restriction	p. 455
Applications	p. 457
Review463
Distance and Approximation	p. 477
Inner Product Spaces	p. 479
Exploration: Vectors and Matrices with Complex Entries	p. 491
Norms and Distance Functions	p. 495
Least Squares Approximation	p. 503
The Singular Value Decomposition	p. 511
Applications	p. 521
Review	p. 527
Key Definitions and Concepts	p. 541
Theorems	p. 565
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