## 2014 - 2015 Spring Semester MATH 3210/5210 Linear Algebra (Barsamian) Final Exam Information

- Exam is on Monday, April 27, 2015, from 10:10am - 12:10pm in Morton 215 (our usual classroom).
- No books or notes.
- No cell phones, calculators, tablets, computers, or other electronic gadgets.
- The Exam is 10 questions, 30 points each, for a total of 300 points.
- The general question topics are shown below. (Some questions are described in more detail than others.)
- Vector Spaces
- Is some given subset a subspace? Some other details are called for, too.

- Solving a Linear System, Particular and Homogeneous Solution: For a given linear system:
- Show the augmented matrix that represents the system.
- Using row operations, find the reduced echelon form of that augmented matrix. Show all details clearly.
- Express the solution set using vectors, with the particular solution and homogeneous solution labeled.
- Check your solution by substitution.

- Linear Independence, Basis, Span, Space Generated by a Set
- Homomorphism & Isomorphism: one of these:
- Either: Are maps
*f,g,h* homomorophisms? Prove yes or state why not.
- Or: Are maps
*f,g,h* isomorophisms? Prove yes or state why not.

- Range Space & Null Space (and Rank & Nullity): For a given map,
- Find the null space and/or range space.
- Find the nullity and/or rank.
- Is the map one-to-one and/or is the map onto?

- Representing linear Maps with Matrices
- represent a linear map as a matrix and use the matrix to compute an output.

- Matrix Multiplication and Matrix Operations
- Matrix Multiplication and Matrix Operations (problem involving summation notation)
- Inverse
- Diagonalization, Eigenvectors, Eigenvalues

**Remark: A significant number of the ten problems will be based on problems from our homework sets and in-class exams!**

(page maintained by Mark Barsamian, last updated April 23, 2015