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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