Outline of topics for Math 2210 Section 10 Summer 2008

Topics may be added or subtracted based on progress in the class and time availble.

Chapter 1: Vectors and the Geometry of Space
- 1.1: Systems of Linear Equations
- 1.2: Row Reduction and Echelon Forms
- 1.3: Vector Equations
- 1.4: The Matrix Equation Ax = b
- 1.5: Solutions Sets to Linear Systems
- 1.7: Linear Independence
- 1.8: Introduction to Linear Transformations
- 1.9: The Matrix of the Linear Tranformations
Chapter 2: Matrix Algebra
- 2.1: Matrix Operations
- 2.2: Inverse of the Matrix
- 2.3: Characterizations of Invertible Matrices
- 2.5: Matrix Factorizations
Chapter 3: Determinants
- 3.1: Introduction to Determinants
- 3.2: Properties of Determinants
- 3.3: Cramer's Rule, Volume, and Linear Transformations
Chapter 4: Vector Spaces
- 4.1: Vector Spaces and Subspaces
- 4.2: Null Spaces, Column Spaces, and Linear Transformations
- 4.3: Linearly Independent Sets: Bases
- 4.4: Coordinate Systems
- 4.5: The Dimension of a Vector Space
- 4.6: Rank
- 4.7: Change of Basis
Chapter 5: Eigenvalues and Eigenvectors
- 5.1: Eigenvalues and Eigenvectors
- 5.2: The Characteristic Equation
- 5.3: Diagonalization
- 5.4: Eigenvectors and Linear Transformations
Chapter 6: Orthogonality and Least Squares
- 6.1: Inner Products, Length, and Orthogonality
- 6.2: Orthogonal Sets