Math 2890 Sample Exam Problems

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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.

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Exam I

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    Solution Sets of Linear Systems
1.7    Linear Independence
1.8    Introduction to Linear Transformations

2.1    Matrix Operations

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Exam II

2.2      The Inverse of a Matrix
2.3      Characterizations of Invertible Matrices
2.4      Partitioned Matrices
2.5      Matrix Factorizations
         Wedderburn Rank Reduction
2.7      Applications to Computer Graphics
2.8      Subspaces of R^n
2.9      Dimension and Rank

3.1      Introduction to Determinants
3.2      Properties of Determinants

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Exam III

3.3      Cramer’s Rule, Volume, and Linear Transformations
 
4.8      Applications to Difference Equations
4.9      Applications to Markov Chains

5.1      Eigenvectors and Eigenvalues
5.2      The Characteristic Equation
5.3      Diagonalization
5.5      Complex Eigenvalues
         Schur Decomposition
5.6      Discrete Dynamical Systems
5.7      Applications to Differential Equations
5.8      Iterative Estimates for Eigenvalues

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Exam IV

6.1      Inner Product, Length, and Orthogonality
6.2      Orthogonal Sets
6.3      Orthogonal Projections
6.4      The Gram-Schmidt Process
         Wedderburn Rank Reduction
6.5      Least-Squares Problems
6.6      Applications to Linear Models

7.1      Diagonalization of Symmetric Matrices
7.2      Quadratic Forms
7.3      Constrained Optimization
7.4      The Singular Value Decomposition
7.5      Applications to Image Processing and Statistics
         The Great Human Diasporas
         Text Retrieval Algorithms

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