The cornerstone of Elementary Linear Algebra is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system.The Sixth Edition incorporates up-to-date coverage of Computer Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding technology guide. Data and applications also reflect current statistics and examples to engage students and demonstrate the link between theory and practice.
Author(s): Ron (Ron Larson) Larson, David C. Falvo
Edition: 6
Publisher: Brooks Cole
Year: 2008
Language: English
Pages: 565
Tags: Математика;Линейная алгебра и аналитическая геометрия;Линейная алгебра;
Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
CONTENTS......Page 6
A WORD FROM THE AUTHORS......Page 10
WHAT IS LINEAR ALGEBRA?......Page 18
1.1 Introduction to Systems of Linear Equations......Page 20
1.2 Gaussian Elimination and Gauss-Jordan Elimination......Page 33
1.3 Applications of Systems of Linear Equations......Page 48
Project 1 Graphing Linear Equations......Page 63
Project 2 Underdetermined and Overdetermined Systems of Equations......Page 64
2.1 Operations with Matrices......Page 65
2.2 Properties of Matrix Operations......Page 80
2.3 The Inverse of a Matrix......Page 92
2.4 Elementary Matrices......Page 106
2.5 Applications of Matrix Operations......Page 117
Project 1 Exploring Matrix Multiplication......Page 139
Project 2 Nilpotent Matrices......Page 140
3.1 The Determinant of a Matrix......Page 141
3.2 Evaluation of a Determinant Using Elementary Operations......Page 151
3.3 Properties of Determinants......Page 161
3.4 Introduction to Eigenvalues......Page 171
3.5 Applications of Determinants......Page 177
Project 1 Eigenvalues and Stochastic Matrices......Page 193
Project 2 The Cayley-Hamilton Theorem......Page 194
Cumulative Test for Chapters 1–3......Page 196
4.1 Vectors in R[sup(n)]......Page 198
4.2 Vector Spaces......Page 210
4.3 Subspaces of Vector Spaces......Page 217
4.4 Spanning Sets and Linear Independence......Page 226
4.5 Basis and Dimension......Page 240
4.6 Rank of a Matrix and Systems of Linear Equations......Page 251
4.7 Coordinates and Change of Basis......Page 268
4.8 Applications of Vector Spaces......Page 281
Project 1 Solutions of Linear Systems......Page 294
Project 2 Direct Sum......Page 295
5.1 Length and Dot Product in R[sup(n)]......Page 296
5.2 Inner Product Spaces......Page 311
5.3 Orthonormal Bases: Gram-Schmidt Process......Page 325
5.4 Mathematical Models and Least Squares Analysis......Page 339
5.5 Applications of Inner Product Spaces......Page 355
Project 1 The QR-Factorization......Page 375
Project 2 Orthogonal Matrices and Change of Basis......Page 376
Cumulative Test for Chapters 4 and 5......Page 378
6.1 Introduction to Linear Transformations......Page 380
6.2 The Kernel and Range of a Linear Transformation......Page 393
6.3 Matrices for Linear Transformations......Page 406
6.4 Transition Matrices and Similarity......Page 418
6.5 Applications of Linear Transformations......Page 426
Project 1 Reflections in the Plane (I)......Page 438
Project 2 Reflections in the Plane (II)......Page 439
7.1 Eigenvalues and Eigenvectors......Page 440
7.2 Diagonalization......Page 454
7.3 Symmetric Matrices and Orthogonal Diagonalization......Page 465
7.4 Applications of Eigenvalues and Eigenvectors......Page 477
Project 1 Population Growth and Dynamical Systems (I)......Page 496
Project 2 The Fibonacci Sequence......Page 497
Cumulative Test for Chapters 6 and 7......Page 498
APPENDIX: MATHEMATICAL INDUCTION AND OTHER A1 FORMS OF PROOFS......Page 500
ANSWER KEY......Page 508
INDEX......Page 558
