Type:
Solution Manual
Resource:
Linear Algebra with Applications
Edition:
10th Edition
Author(s):
Steven Leon Lisette de Pills
INSTRUCTOR’S SOLUTIONS MANUAL L INEAR ALGEBRA WITH A PPLICATIONS TENTH EDITION
Steven J. Leon University of Massachusetts Dartmouth
Lisette G. de Pillis Harvey Mudd College
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 © 2020, 2015, 2010 by Pearson Education, Inc. 221 River Street, Hoboken, NJ 07030. All rights reserved. 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: 978-0-13-526050-0 ISBN-10: 0-13-526050-7
Contents Preface
v
1 Matrices and Systems of Equations 1 2 3 4 5 6
Systems of Linear Equations Row Echelon Form Matrix Arithmetic Matrix Algebra Elementary Matrices Partitioned Matrices MATLAB Exercises Chapter Test A Chapter Test B
2 Determinants 1 2 3
The Determinant of a Matrix Properties of Determinants Additional Topics and Applications MATLAB Exercises Chapter Test A Chapter Test B
30 33 36 38 38 39 42
Definition and Examples Subspaces Linear Independence Basis and Dimension Change of Basis Row Space and Column Space MATLAB Exercises Chapter Test A Chapter Test B
4 Linear Transformations 1 2 3
1 2 3 7 12 18 22 24 27 30
3 Vector Spaces 1 2 3 4 5 6
1
Definition and Examples Matrix Representations of Linear Transformations Similarity MATLAB Exercise
42 46 52 55 57 57 65 66 68 72 72 75 78 79 iii
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iv
Contents
Chapter Test A Chapter Test B
80 81
5 Orthogonality 1 2 3 4 5 6 7
84 n
The Scalar product in R Orthogonal Subspaces Least Squares Problems Inner Product Spaces Orthonormal Sets The Gram-Schmidt Process Orthogonal Polynomials MATLAB Exercises Chapter Test A Chapter Test B
6 Eigenvalues 1 2 3 4 5 6 7 8
119
Eigenvalues and Eigenvectors Systems of Linear Differential Equations Diagonalization Hermitian Matrices Singular Value Decomposition Quadratic Forms Positive Definite Matrices Nonnegative Matrices MATLAB Exercises Chapter Test A Chapter Test B
7 Numerical Linear Algebra 1 2 3 4 5 6 7 8
84 86 89 93 99 107 109 112 113 115
Floating-Point Numbers Gaussian Elimination Pivoting Strategies Matrix Norms and Condition Numbers Orthogonal Transformations The Eigenvalue Problem Least Squares Problems Iterative Methods MATLAB Exercises Chapter Test A Chapter Test B
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119 124 125 133 141 143 146 149 152 154 156 160 160 161 162 163 174 175 179 182 183 185 186