## 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.)
1. Vector Spaces
• Is some given subset a subspace? Some other details are called for, too.
2. 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.
3. Linear Independence, Basis, Span, Space Generated by a Set
4. 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.
5. 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?
6. Representing linear Maps with Matrices
• represent a linear map as a matrix and use the matrix to compute an output.
7. Matrix Multiplication and Matrix Operations
8. Matrix Multiplication and Matrix Operations (problem involving summation notation)
9. Inverse
10. 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