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Linear Algebra And Its Applications 6th Edition Solutions Manual PDF

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  • Course
  • MATH101
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  • University Of San Andrés (UdeSA )
  • Book
  • 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.

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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.

Copyright © 2021 by Pearson Education, Inc., 221 River Street, Hoboken, NJ 07030. All rights reserved.

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


iii
Copyright © 2021 Pearson Education, Inc.

, 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

Chapter 8 The Geometry of Vector Spaces 8-1
8.1 Affine Combinations 8-1
8.2 Affine Independence 8-5
8.3 Convex Combinations 8-10
8.4 Hyperplanes 8-15
8.5 Polytopes 8-19
8.6 Curves and Surfaces 8-22
Supplementary Exercises 8-27

Chapter 9 Optimization 9-1
9.1 Matrix Games 9-1
9.2 Linear Programming—Geometric Method 9-7
9.3 Linear Programming—Simplex Method 9-11
9.4 Duality 9-15
Supplementary Exercises 9-22


iv
Copyright © 2021 Pearson Education, Inc.

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