Instructor: Atzberger

Worksheets

• Systems of Linear Equations
• The Row Reduction Algorithm
• Vector Equations
• Matrix-Vector Products
• Solution Sets of Linear Systems
• Applications of Linear Systems (not handed out in section)
• Linear Independence
• Linear Transformations
• The Matrix of a Linear Transformation
• Matrix Operations
• The Inverse of a Matrix
• Characterizing Invertible Matrices
• Subspaces of R^n
• Determinants!
• Determinants II: Return of Row Operations
• Vector Spaces
• Column and Null Spaces
• Bases
• Coordinates (not handed out in section)
• Dimension and Rank (not handed out in section)
• Eigenvalues
• Eigenvalues and Where to Find Them
• Inner (Dot) Products, Length, and Orthogonality

Solutions

• Systems of Linear Equations
• The Row Reduction Algorithm
• Vector Equations
• Matrix-Vector Products
• Solution Sets of Linear Systems
• Applications of Linear Systems
• Linear Independence
• Linear Transformations
• The Matrix of a Linear Transformation
• Matrix Operations
• Determinants!
• Determinants II: Return of Row Operations
• Vector Spaces
• Column and Null Spaces
• Bases
• Coordinates (not handed out in section)
• Dimension and Rank (not handed out in section)
• Eigenvalues
• Eigenvalues and Where to Find Them
• Inner (Dot) Products, Length, and Orthogonality

Supplemental Material

• Equivalent Systems
• Numerical Methods—Jacobi and Gauss-Seidel Iteration
• Practice Final 5c Solution Extended