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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