Linear Algebra and Its Applications: Pearson International Edition
Complete Solutions Manual PDF for Linear Algebra And Its Applications 6th Edition by David C. Lay, Steven R. Lay and Judi J. McDonald. Includes answers for all 9 chapters of the book.
Class notes Linear Algebra (MATH1554) Linear Algebra and Its Applications, ISBN: 9781292020556
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INSTRUCTOR’S
SOLUTIONS MANUAL
LINEAR ALGEBRA
AND ITS APPLICATIONS
SIXTH EDITION
David C. Lay
University of Maryland–College Park
Steven R. Lay
Lee University
Judi J. McDonald
Washington State University
,
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and
publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation
contained in this book. The author and publisher shall not be liable in any event for incidental or consequential
damages in connection with, or arising out of, the furnishing, performance, or use of these programs.
Reproduced by Pearson from electronic files supplied by the author.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any
means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the
publisher. Printed in the United States of America.
ISBN-13: 978-0-13-586609-2
ISBN-10: 0-13-586609-X
, Contents
Introduction v
Chapter 1 Linear Equations in Linear Algebra 1-1
1.1 Systems of Linear Equations 1-1
1.2 Row Reduction and Echelon Forms 1-8
1.3 Vector Equations 1-16
1.4 The Matrix Equation Ax = b 1-25
1.5 Solution Sets of Linear Systems 1-33
1.6 Applications of Linear Systems 1-42
1.7 Linear Independence 1-51
1.8 Introduction to Linear Transformations 1-58
1.9 The Matrix of a Linear Transformation 1-65
1.10 Linear Models in Business, Science, and Engineering 1-71
Supplementary Exercises 1-80
Chapter 2 Matrix Algebra 2-1
2.1 Matrix Operations 2-1
2.2 The Inverse of a Matrix 2-7
2.3 Characterization of Invertible Matrices 2-15
2.4 Partitioned Matrices 2-23
2.5 Matrix Factorizations 2-32
2.6 The Leontief Input-Output Model 2-47
2.7 Applications to Computer Graphics 2-51
2.8 Subspaces of n 2-58
2.9 Dimension and Rank 2-66
Supplementary Exercises 2-72
Chapter 3 Determinants 3-1
3.1 Introduction to Determinants 3-1
3.2 Properties of Determinants 3-8
3.3 Cramer’s Rule, Volume, and Linear Transformations 3-14
Supplementary Exercises 3-22
Chapter 4 Vector Spaces 4-1
4.1 Vector Spaces and Subspaces 4-1
4.2 Null Spaces, Column Spaces, Row Spaces, and Linear Transformations 4-7
4.3 Linearly Independent Sets; Bases 4-15
4.4 Coordinate Systems 4-23
4.5 The Dimension of a Vector Space 4-30
4.6 Change of Basis 4-36
4.7 Digital Signal Processing 4-40
4.8 Applications to Difference Equations 4-43
Supplementary Exercises 4-52
, Chapter 5 Eigenvalues and Eigenvectors 5-1
5.1 Eigenvalues and Eigenvectors 5-1
5.2 The Characteristic Equation 5-10
5.3 Diagonalization 5-15
5.4 Eigenvalues and Linear Transformations 5-29
5.5 Complex Eigenvalues 5-35
5.6 Discrete Dynamical Systems 5-43
5.7 Applications to Differential Equations 5-49
5.8 Iterative Estimates for Eigenvalues 5-59
5.9 Applications to Markov Chains 5-67
Supplementary Exercises 5-75
Chapter 6 Orthogonality and Least Squares 6-1
6.1 Inner Product, Length, and Orthogonality 6-1
6.2 Orthogonal Sets 6-5
6.3 Orthogonal Projections 6-10
6.4 The Gram-Schmidt Process 6-18
6.5 Least-Squares Problems 6-24
6.6 Machine Learning and Linear Models 6-29
6.7 Inner Product Spaces 6-34
6.8 Applications of Inner Product Spaces 6-38
Supplementary Exercises 6-43
Chapter 7 Symmetric Matrices and Quadratic Forms 7-1
7.1 Diagonalization of Symmetric Matrices 7-1
7.2 Quadratic Forms 7-14
7.3 Constrained Optimization 7-22
7.4 The Singular Value Decomposition 7-27
7.5 Applications to Image Processing and Statistics 7-37
Supplementary Exercises 7-40
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