Math 2890 Sample Exam Problems

---

These problems are designed to be worked while online. They require javascript to be enabled.

Chapter and section numbers are from Linear Algebra and its applications (4/e) by David C. Lay.

---

Chapter 1

1. Systems of Linear Equations
2. Row Reduction and Echelon Forms
3. Vector Equations
4. The Matrix Equation Ax = b
5. Solution Sets of Linear Systems
6. Linear Independence
7. Introduction to Linear Transformations

Chapter 2

1. Matrix Operations
2. The Inverse of a Matrix
3. Characterizations of Invertible Matrices
4. Partitioned Matrices
5. Matrix Factorizations
   Wedderburn Rank Reduction

7. Applications to Computer Graphics
8. Subspaces of `R^n`
9. Dimension and Rank

Chapter 3

1. Introduction to Determinants
2. Properties of Determinants
3. Cramer’s Rule, Volume, and Linear Transformations

Chapter 4

8. Applications to Difference Equations
9. Applications to Markov Chains

Chapter 5

1. Eigenvectors and Eigenvalues
2. The Characteristic Equation
3. Diagonalization

5. Complex Eigenvalues
6. Discrete Dynamical Systems
7. Applications to Differential Equations
8. Iterative Estimates for Eigenvalues

Chapter 6

1. Inner Product, Length, and Orthogonality
2. Orthogonal Sets
3. Orthogonal Projections
4. The Gram-Schmidt Process
   Wedderburn Rank Reduction
5. Least-Squares Problems
6. Applications to Linear Models

Chapter 7

1. Diagonalization of Symmetric Matrices
   Schur Decomposition
2. Quadratic Forms
3. Constrained Optimization
4. The Singular Value Decomposition
5. Applications to Image Processing and Statistics
   The Great Human Diasporas
   Text Retrieval Algorithms

---

Back to Linear Algebra or home page.

---