Linear Algebra For Dummies [Paperback]

An easy-to-follow guide to practical, real-world applications of linear algebra

Linear algebra is a branch of mathematics that uses matrices to solve systems of linear equations; it has applications in many disciplines, from sociology and game theory to computer programming, engineering, and business. Linear Algebra For Dummies maps to a typical, college-level linear algebra course, in which students first study matrices and matrix operations, then apply those fundamentals to abstract topics such as vector spaces, linear transformations, determinants, and, finally, eigenvalues and eigenvectors. It gives students theoretical and practical ways of approaching various types of problems, presenting the information in a way that allows readers to fully digest not just the how of solving linear algebraic problems, but also the why.

Introduction 1

Part I: Lining Up the Basics of Linear Algebra 7

Chapter 1: Putting a Name to Linear Algebra 9

Chapter 2: The Value of Involving Vectors 19

Chapter 3: Mastering Matrices and Matrix Algebra 41

Chapter 4: Getting Systematic with Systems of Equations 65

Part II: Relating Vectors and Linear Transformations 85

Chapter 5: Lining Up Linear Combinations 87

Chapter 6: Investigating the Matrix Equation Ax = b 105

Chapter 7: Homing In on Homogeneous Systems and Linear Independence 123

Chapter 8: Making Changes with Linear Transformations 147

Part III: Evaluating Determinants 173

Chapter 9: Keeping Things in Order with Permutations 175

Chapter 10: Evaluating Determinants 185

Chapter 11: Personalizing the Properties of Determinants 201