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Lecture Notes for Math 220 Section 4

 Date Topics 1/9/18 Introduction, Review of Systems of Linear Equations 1/11/18 Systems of Linear Equations (continued), Matrices 1/16/18 Elementary Row Operations, Row Reduction and Echelon Forms, Pivot Positions 1/18/18 Uniqueness of Reduced Echelon Form, Existence and Uniqueness of Solutions 1/23/18 Vectors in n-dimensional space, Linear Combinations, The Span of a Set of Vectors 1/25/18 The Matrix Equation Ax=b, Existence of Solutions of Ax=b 1/30/18 Solution Sets of Linear Systems, Homogeneous and Nonhomogeneous Systems, Solution Sets in Parametric Vector Form 2/1/18 Linear Independence 2/6/18 Span and Linear Independence (Pop Quiz), Linear Transformations 2/8/18 More on Linear Transformations, One-to-one and Onto Mappings 2/13/18 Matrix Operations 2/15/18 The Inverse of a Matrix 2/20/18 The Invertible Matrix Theorem 3/6/18 Vector Spaces, Subspaces, The Column Space of a Matrix 3/8/18 The Null Space of a Matrix, Bases 3/20/18 More on Bases, Dimension and Rank 3/22/18 (Part 1) Determinants 3/22/18 (Part 2) Properties of Determinants 3/27/18 Properties of Determinants, Eigenvectors and Eigenvalues 3/29/18 Eigenvalues and Eigenvectors (Continued), The Characteristic Equation 4/3/18 Inner Product, Length, Orthogonality, Orthogonal Subspaces 4/5/18 Orthogonal & Orthonormal Sets, Orthogonal Basis, Orthogonal Projections 4-10-18 Orthogonal Matrices, The Orthogonal Decomposition Theorem, The Best Approximation Theorem