A First Course in Linear Algebra with Applications

by Yaqub; Moore

• ISBN13: 9780125057608
• ISBN10: 0125057601
• Edition: 3rd
• Format: Hardcover
• Copyright: 1998-03-18
• Publisher: Elsevier Science
• More Book Details

Summary

This text intends to transform students from passive observers of mathematics to participants in it. The book employs a spiral development of ideas to blend the requirements of problem solving, analytical thinking, computational technique, and applications, and emphasizes the interplay of algebraic and geometric concepts. It includes an extensive number of exercises, ranging from routine to challenging. The Third Edition offers 40 percent new material, including manynew applications. It incorporates MATLAB to demonstrate how computational software tools can be used in this field. * Offers a proven, successful approach to Linear Algebra * Contains a practical presentation, illuminating examples, and exceptional exercises, thus enabling instructors to emphasize computational techniques, theoretical material, and applications * Includes a wide variety of effective applications * Provides a student friendly writing style * Begins with the familiar and proceeds to the new in a well-motivated manner * Acknowledges current reforms and proceeds from there * Explains how to solve some examples in MATLAB, demonstrating how such software tools can be used in this field * Includes student projects at close of chapter exercise sets

Table of Contents

Preface	vii	(6)
To the Student	xiii
Chapter 1. Systems of Linear Equations and Matrices	1	(52)
1.1 Systems of Linear Equations -- Matrix Methods	2	(18)
1.2 Linear Systems without Unique Solutions	20	(15)
1.3 Applications -- Algorithms	35	(14)
Chapter 1. Review and Supplementary Exercises and Projects	49	(4)
Chapter 2. Matrix Algebra	53	(96)
2.1 Matrix Arithmetic	53	(14)
2.2 Matrix Multiplication	67	(16)
2.3 Matrix Inverses	83	(22)
2.4 Partitioned Matrices	105	(11)
2.5 Factorization	116	(12)
2.6 Applications -- Networks and Graphs	128	(14)
Chapter 2. Review and Supplementary Exercises	142	(7)
Chapter 3. Matrix and Vector Equations	149	(94)
3.1 Vectors in Euclidean n-Space	150	(16)
3.2 Distance, Angle, and Dot (Inner) Products in Euclidean n-Space	166	(15)
3.3 Linear Dependence and Independence	181	(17)
3.4 Linear Transformations	198	(14)
3.5 Applications	212	(21)
Chapter 3 Review Exercises	233	(2)
Chapter 3 Supplementary Exercises and Projects	235	(8)
Chapter 4. Determinants	243	(74)
4.1 The Determinant Function and Cramer's Rule	244	(13)
4.2 Laplace Expansion of Determinants	257	(9)
4.3 Properties of Determinants	266	(12)
4.4 Determinants and Matrix Inversion	278	(8)
4.5 Cross Products in R(3) (Optional)	286	(13)
4.6 Eigenvalues and Eigenvectors of a Matrix	299	(7)
Chapter 4 Review Exercises	306	(1)
Chapter 4 Supplementary Exercises and Projects	307	(10)
Chapter 5. Vector Spaces	317	(70)
5.1 Vector Spaces and Linear Combinations	317	(16)
5.2 Subspaces, Ordered Basis, and Dimension	333	(15)
5.3 Linear Transformations, Kernel, and Range	348	(17)
5.4 Matrices -- Row and Column Spaces, Rank	365	(12)
Chapter 5 Review Exercises	377	(2)
Chapter 5 Supplementary Exercises and Projects	379	(8)
Chapter 6. Inner-Product Spaces	387	(66)
6.1 Real Inner Products	387	(14)
6.2 Geometry in Real Inner-Product Spaces	401	(14)
6.3 Constructing an Orthonormal Basis: Gram-Schmidt	415	(16)
6.4 Complex Vector, Matrices, Inner Products	431	(13)
Chapter 6 Review Exercises	444	(1)
Chapter 6 Supplementary Exercises and Projects	445	(8)
Chapter 7. Coordinates, Matrices, and Transformations	453	(66)
7.1 Coordinates and Change of Basis	454	(11)
7.2 Matrix Representation of Transformations, Similarity	465	(21)
7.3 Orthogonal Matrices and Transformations	486	(8)
7.4 Markov Chains	494	(17)
Chapter 7 Review Exercises	511	(1)
Chapter 7 Supplementary Exercises and Projects	512	(7)
Chapter 8. Eigenspaces and Applications of Eigenvalue Theory	519	(80)
8.1 Eigenvectors, Eigenvalues, and Eigenspaces	520	(15)
8.2 Similarity to a Diagonal Matrix	535	(14)
8.3 Real Symmetric Matrices	549	(8)
8.4 Complex Matrices and Eigenvalues	557	(11)
8.5 Quadratic Forms, Conics	568	(9)
8.6 Quadric Surfaces	577	(8)
8.7 Systems of Differential Equations	585	(6)
Chapter 8 Review Exercises	591	(1)
Chapter 8 Supplementary Exercises and Projects	592	(7)
Appendix	599	(32)
A.1 The Complex Numbers	599	(5)
A.2 Sets and Functions	604	(11)
A.3 Methods of Proof	615	(16)
References	631
Answers to Odd-Numbered Exercises	A-1
Index	I-1