Math 2890 Sample Exam Problems
These problems are designed to be worked while online. They require javascript to be enabled in a browser that supports MathML. I recommend Mozilla/Firefox.
Chapter and section numbers are from Linear Algebra and its applications (3/e update) by David C. Lay.
Chapter 1
- Systems of Linear Equations
- Row Reduction and Echelon Forms
- Vector Equations
- The Matrix Equation Ax = b
- Solution Sets of Linear Systems
- Linear Independence
- Introduction to Linear Transformations
Chapter 2
- Matrix Operations
- The Inverse of a Matrix
- Characterizations of Invertible Matrices
- Partitioned Matrices
- Matrix Factorizations
Wedderburn Rank Reduction
- Applications to Computer Graphics
- Subspaces of `R^n`
- Dimension and Rank
Chapter 3
- Introduction to Determinants
- Properties of Determinants
- Cramer’s Rule, Volume, and Linear Transformations
Chapter 4
- Applications to Difference Equations
- Applications to Markov Chains
Chapter 5
- Eigenvectors and Eigenvalues
- The Characteristic Equation
- Diagonalization
- Complex Eigenvalues
- Discrete Dynamical Systems
- Applications to Differential Equations
- Iterative Estimates for Eigenvalues
Chapter 6
- Inner Product, Length, and Orthogonality
- Orthogonal Sets
- Orthogonal Projections
- The Gram-Schmidt Process
Wedderburn Rank Reduction - Least-Squares Problems
- Applications to Linear Models
Chapter 7
- Diagonalization of Symmetric Matrices
Schur Decomposition - Quadratic Forms
- Constrained Optimization
- The Singular Value Decomposition
- Applications to Image Processing and Statistics
The Great Human Diasporas
Text Retrieval Algorithms
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