Linear Algebra and Its Applications -- Student Study Guide, 5th Edition(线性代数及其应用——学生学习指南,第5版).pdf

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Linear Algebra and Its Applications -- Student Study Guide, 5th Edition.pdf
Contents INTRODUCTION vi Technology Support vi Review materials on the Web vii HOW TO STUDY LINEAR ALGEBRA viii CHAPTER 1 LINEAR EQUATIONS IN LINEAR ALGEBRA 1.1 Systems of Linear Equations 1-1 1.2 Row Reduction and Echelon Forms 1-7 1.3 Vector Equat 1. 4 The Matrix Equation Ax=b 1-15 1.5 Solution Sets of Linear Systems 1-19 1.6 Applications of Linear Systems 1-24 1.7 Linear Independence 1-28 1. 8 Introduction to linear transformations 1-31 1.9 Matrix of a Linear transformation 1-35 1.10 Linear Models in Business, Science, and Engineering 1-39 Supplementary Exercises 1-43 Glossary checklist 1-44 CHAPTER 2 MATRIX ALGEBRA 2.1 Matrix Operations 2-1 2.2 The Inverse of a matrix 2 2.3 Characterization of Invertible Matrices 2-9 2. 4 Partitioned matrices 2-14 2.5 Matrix Factorizations 2-20 2.6 The Leontief Input-Output Model 2-28 2.7 Applications to computer graphics 2-30 2.8 Subspaces ofR" 2-33 2.9 Dimension and rank 2-38 Supplementary Exercises 2-42 Glossary Checklist 2-42 CHAPTER 3 DETERMINANTS 3.1 Introduction to determinants 3 3.2 Properties of Determinants 3-5 3. 3 Cramer's Rule Volume and Linear trans formations 3-8 Glossary Checklist 3-13 CHAPTER 4 VECTOR SPACES 4.1 Vector Spaces and Subspaces 4-1 4.2 Null Spaces, Column Spaces, and Linear Transformations 4-4 4.3 Linearly Independent Sets; Bascs 4-7 4.4 Coordinate Systems 4-10 4.5 The Dimension of a Vector Space 4-16 4.6Rank4-18 4.7 Cha f Basis 4-23 4.8 Applications to Difference Equations 4-27 4.9Ap pplications to markov chains 4-32 Glossary Checklist 4-34 CHAPTER 5 EIGENVALUES AND EIGENVECTORS 5.1 Eigenvectors and Eigenvalues 5-1 5.2 The Characteristic Equation 5-5 5.3 Diagonalization 5-10 5.4 Eigenvectors and Linear Transformations 5-15 5.5 Complex Eige envalues 5-19 5.6 Discrete Dynamical Systems 5-22 5.8 Iterative Estimates for Eigenvalues 5-28 o 5.7 Applications to Differential Equations 5-2 Glossary Checklist 5-33 CHAPTER 6 ORTHOGONALITY AND LEAST SQUARES 6.1 Inner Product, Length, and Orthogonality 6-1 6.2 Orthogonal Sets 6-3 6.3 Orthogonal Projections 6-5 6.4 The Gram-Schmidt Process 6-9 6.5 Least-Squares problems 6-13 6.6 Applications to Lincar Models 6-16 6.7 Inner product Spaces 6-20 6.8 Applications of Inner product Spaces 6-23 Glossary Checklist 6-26 CHAPTER 7 SYMMETRIC MATRICES AND QUADRATIC FORMS 7.1 Diagonalization of Symmetric matrices 7-1 7.2 Quadratic Forms 7-5 7.3 Constrained Optimization 7-8 7. 4 The Singular Value Decomposition 7-10 7.5 Applications to Image Processing and Statistics 7-16 Supplementary Exercises 7-19 Glossary Checklist 7-19 CHaPTER 8 THE GEOMETRY OF VECTOR SPaces 8.1 Affine combinations 8-1 8.2 Affine Independence 8-4 8. 3 Convex Combinations 8-7 8.4 Hyperplanes 8-9 8.5 Polytopes 8-12 8.6 Curves and surfaces 8-14 Glossary Checklist 8-16 TECHNOLOGY INDEX OF PRODCEDURES AND TERMS TECH-1 APPENDICES INTRODUCTION TO MATLAB Getting Started With matlab ML-1 Script m-Files ML-4 Index of matlab Commands ML-6 NOTES FOR THE MAPLE COMPUTER ALGEBRA SYSTEM Getting Started With Maple MP-1 Study guide notes MP-5 Index of Maple Commands MP-25 NOTES FOR THE MATHEMATICA COMPUTER ALGEBRA SYSTEM Getting Started With Mathematica MM-1 Study guide notes Mm Index of mathematica Commands MM-29 NOTES FOR THE T1-83+84+/89 GRAPHIC CALCULATORS Getting Started with a TI-83+ Calculator TI-1 Getting Started with a TI-84+ Calculator TI-2 Getting Started with a TI-89 Calculator TI-2 Study Guide ne Index of Ti-84 Family Commands TI-22 Index of ti-89 Commands TI-23 INTRODUCTION This Study guide is designed to help you succeed in your linear algebra course. It shows you how to study mathematics, to learn new material, and to prepare effective review sheets for tests Key Ideas and Study notes guide you through each section, with summaries of important ideas and tables that connect related ideas. Detailed solutions to hundreds of exercises (usually every third odd exercise)allow you to check your work or help you get started on a difficult problem also, complete explanations are provided for each writing exercise whose answer in the text is only a"Hint. Study Tips point out important exercises, give hints about what to study, and sometimes highlight potential exam questions. Frequent Warnings identify common student errors. Don t ever take an exam without reviewing these warnings The most important material in this Study Guide is on pages vii through ix of this introduction. Students who follow the strategies in How to Study linear algebra invariably achieve remarkable results in this course. you can be one of those students TECHNOLOGY SUPPORT If you are using technology with your course, you will need this Study Guide. Besides its valuable support for the course material the guide includes"Lab manuals "for three computer programs and three graphic calculators. Everything you need to know about using this technology with your text is here. New commands are introduced gradually, and detailed instructions are given for their use. Also, data for more than 850 exercises from the text are stored in electronic files for each type of technology. You' ll save hours of time and avoid errors n typing. The files also contain special programs that reinforce basic concepts in the course. If the school computer system or in specified labs. If you are using a TI-83+, TI-84+, or TI-89 On your class is using MATLAB, Maple, or Mathematica, your files are probably already loaded your instructor may have plans to download the files to your calculator. In any case, you can always download the files yourself from the Web site it into your calculator. The files on the Web will always reflect the latest versions available. oad A ReadMe file with each data set describes how to incorporate the data into your software or le Special matlab boxes at the ends of many Study Guide sections explain how to use MATLAB for your homework, introducing simple commands as they are needed for the exercises. The first appendix at the back of the Guide contains a quick introduction, Getting Started with MatlaB, and an index of matlab commands i encourage you to try MATLAB--it is easy to learn Notes for the Maple and mathematica computer algebra systems and for the T1-83+84+/89 graphic calculators are included in the last three appendices to this Study Guide. The notes correspond to the matlab boxes and translate MatlaB commands into syntax appropriate for the other technologies. Each set of notes has its own index. Whenever you see a matlab box in this Guide, turn to the appropriate appendix for help with your technology The following faculty members wrote the notes and developed the data sets Maple Douglas meade, University of South Carolina, Columbia, sC Mathematica: Maric Vanisko. Carroll College. MT TI-83+/84+/89: Michael Miller, Corban University, salem, OR MATLAB Jeremy case, taylor university, Marion, IN These colleagues have given good advice based on teaching with our text and Study Guide. I appreciate their contributions to this revision of the Study Guide REVIEW MATERIALS ON THE WEB In addition to the help in this Study guide, i have provided some material on the Web that my stu dents really appreciate--review sheets and practice exams. Please heed the advice below, because using these study aids in the wrong way can lcad to a disaster at exam time. I suggest four steps to prepare for each exam 1. Assemble a review sheet. The Web review sheets reflect what i emphasize in my courses. If possible, you need to find out what your instructor expects of you. The three courses on the Web material vary somewhat in their content and approach, and they organize the material differently. To construct a review sheet for one of your exams, you may need to combine parts of two sheets from the Web 2. Try to complete an initial review for an exam a day or two early. Hard to do, but worth the effort. Don't read the sample exams! Studying from an old exam is a big mistake. Instead study your lecture notes, looking for items that were emphasized in class. Read over your homework and old quizzes. I insist that my students learn key definitions, practically word for word. If they cannot write a definition properly, they dont know what they are writing about 3. After the review, take the sample exam whose subject material most closely fits what your exam will cover. Find a quiet place and time when you can work the entire exam without stopping and without looking at the text or your notes.(Of course, skip any questions that are inappropriate for your course. Write your answers. Time yourself. 4. Finally after you have completed the test, look at the solutions. Identify the areas that need further review. If possible, find an example in the text related to an area in which you are weak. Cover up the solution to the example, and try to write out the solution yourself. Peek if necessary. Don't be reluctant to ask for help HOW TO STUDY LINEAR ALGEBRA A first course in linear algebra is dramatically different from most mathematics courses that pre cede it. The focus shifts from learning computational procedures to digesting and mastering basic concepts that underlie the computations. To survive, you may need to learn a new way to study mathematics. That's why I wrote this Study Guide-to show you how to succeed in the course and to give you tools to do this Because you are likely to use linear algebra later in your career, you need to learn the material at a level that will carry you far beyond the final exam. I believe that the strategies below are crucial to success Strategies for Success in Linear algebra 1. Study before you start to work on exercises. Most students dont do this in courses that precede linear algebra. They survive by looking at the examples when they cannot solve an exercise. That simply will not work in linear algebra. If you"copy an example(with neces- sary modifications), you may think you understand the problem, but very little true learning has taken place. (You'll find that out on your first exam. For this course, in addition to knowing how to carry out a certain procedure, you must learn when that procedure is appro priate and (most importantly)why it work For success with homework, read the text section first, perhaps taking a few notes. Then read the Key Ideas or Study Notes in the Study Guide for that section. Finally, start to work on the assigned exercises. In the long run, this approach will improve your performance and save you time. The preparation time spent here will greatly reduce your exam preparation time 2. Prepare for each class period as you would for a language class. Mastery of the subject requires that you learn a rich vocabulary. Your goal now is to become so familiar with con cepts that you can use them easily(and correctly)in conversation and in writing. For home work, try to write complete sentences, such as you'll find the Study guide solutions. Pay attention, too, to the warnings here about misuse of terminology This course resembles a language course because of the preparation needed between class meetings, to avoid falling behind. Most sections in the text build on preceding sections Once you are behind, catching up with the class is often difficult. The fact that concepts may seem"simple?"does not mean that you can afford to postpone your study until the weekend The homework may be harder than you expect The most valuable advice I can give is to keep up with the course 3. Concentrate more on learning definitions, facts, and concepts, than on practicing routine computations or algorithms. Pay attention to connections between concepts. Many theorems and boxed"facts"describe such connections. For examples, see Theorem 2 in Section 1.2 and Theorems 3 and 4 in Section 1.4. Your goal is to think in general terms, to imagine typical computations without performing any arithmetic, and to focus on the principles behind the computations 4. Review frequently. Review and reflection are key ingredients for success in learning the material. At strategic points in this Guide, I have inserted special subsections labeled Mastering Lincar Algebra Concepts. They provide specific help for your review of cach main concept. I urge you to prepare the review sheets described as you reach each review point. Later, you may choose to add further notes. of course, use the sheets to review for exams. A Glossary Checklist at the end of each chapter in the Guide may help you learn important definitions caution Because you can find complete solutions here to many exercises, you will be tempted to read the explanations before you really try to write out the solutions yourself. Dont do it! If you merely think a bit about a problem and then check to see if your idea is basically correct, you are likely to overestimate your understanding. Some of my students have done this and miserably failed the first exam. By then the damage was done, and they had great difficulty catching up with the class. Proper use of the Study Guide, however, will help you succeed and enjoy the course at the same time A Personal note Students who have used this material have told me how much it helped them learn linear algebra and prepare for tests. The first time my students used the Study Guide notes, they had already taken one exam. Grades on the next exam were substantially higher For some students, the improvement was dramatic. I hope the Study Guide will encourage you to master linear algebra and to perform at a level higher than you ever dreamed possible David C. L

试读 127P Linear Algebra and Its Applications -- Student Study Guide, 5th Edition(线性代数及其应用——学生学习指南,第5版).pdf
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qq_41275034 lay 第五版的 谢谢
jxsdxc 非常好,很经典的线性代数书!
lad1984 非常好的资源,是文本,不是扫描
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