Fundamentals of Matrix Algebra 3rd Edition 1

Thanks......Page 5 Preface......Page 7 Table of Contents......Page 9 1.1 Introduction to Linear Equations......Page 11 1.2 Using Matrices To Solve Systems of Linear Equations......Page 15 1.3 Elementary Row Operations and Gaussian Elimination......Page 22 1.4 Existence and Uniqueness of Solutions......Page 32 1.5 Applications of Linear Systems......Page 44 2.1 Matrix Addition and Scalar Multiplication......Page 55 2.2 Matrix Multiplication......Page 61 2.3 Visualizing Matrix Arithmetic in 2D......Page 76 2.4 Vector Solutions to Linear Systems......Page 90 2.5 Solving Matrix Equations AX=B......Page 107 2.6 The Matrix Inverse......Page 113 2.7 Properties of the Matrix Inverse......Page 122 3.1 The Matrix Transpose......Page 131 3.2 The Matrix Trace......Page 141 3.3 The Determinant......Page 145 3.4 Properties of the Determinant......Page 156 3.5 Cramer's Rule......Page 169 4.1 Eigenvalues and Eigenvectors......Page 173 4.2 Properties of Eigenvalues and Eigenvectors......Page 187 5.1 Transformations of the Cartesian Plane......Page 197 5.2 Properties of Linear Transformations......Page 212 5.3 Visualizing Vectors: Vectors in Three Dimensions......Page 225 A Solutions To Selected Problems......Page 237 Index......Page 247