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Lecture Notes for Math 220 Section 1

 Notes Topics 8/30/16 Row Reduction and Echelon Forms, Pivot Positions, Uniqueness of Reduced Echelon Form 9/1/16 Existence and Uniqueness of Solutions, Vectors in n-dimensional space, Linear Combinations 9/6/16 Linear Combinations (continued), The Span of a Set of Vectors, The Matrix Equation Ax=b 9/8/16 Existence of Solutions of Ax=b, Solution Sets of Linear Systems, Homogeneous and Nonhomogeneous Systems 9/13/16 Solution Sets in Parametric Vector Form, Linear Independence 9/15/16 Span and Linear Independence, Linear Transformations, Dilation and Contraction Operators, Rotation Operators 9/20/16 Linear Transformations (continued), One-to-one and Onto Mappings 9/22/16 One-to-one and Onto Mappings (continued), Matrix Operations 9/27/16 Review for Exam 1 9/29/16 Powers of a Matrix, Shear Transformations, The Inverse of a Matrix 10/4/16 Elementary Matrices, The Invertible Matrix Theorem, Invertible Linear Transformations 10/6/16 Invertible Linear Transformations (continued), Subspaces of n-dimensional real vector space 10/11/16 Recap of Linear Transformations, Subspaces of n-dimensional real vector space (continued) 10/13/16 The Column Space and Null Space of a Matrix, Basis for a Subspace 10/18/16 Basis for the Column Space of a Matrix, Basis for the Null Space of a Matrix, Dimension and Rank 10/20/16 The Rank Theorem, The Basis Theorem, The Invertible Matrix Theorem (more results) 10/25/16 Determinants 10/27/16 Properties of Determinants 11/1/16 Review for Exam 2 11/8/16 Eigenvectors and Eigenvalues 11/10/16 The Characteristic Equation 11/15/16 The Invertible Matrix Theorem (more results), Similarity of Matrices 11/17/16 Inner Product, Length, and Orthogonality, Orthogonal Subspaces 11/29/16 Orthogonal Sets, Orthogonal Basis, Orthogonal Projections 12/1/16 Orthogonal Projections (continued), The Gram-Schmidt Process 12/8/16 Review for the Final Exam