Math 341 Final Exam Preparation
Blank Exams and Exam Solutions:
Essential Exam Exercises: These are exercises from each exam that form the heart of what we've studied.
- Exam 1: 5, 7, 8, 9, 10
- Exam 2: 1, 4, 5, 8, 9, 10, 11
- Exam 3: 1 - 13 all
Anything we did on exams, assignments or in class is "fair game" on the final, but you should start with the above things in your studying. Then make sure you also know about
Eigenvalues and Eigenvectors:
- You should be able to determine whether a given vector is an eigenvector and, if it is, what the corresponding eigenvalue is. Assignment 13 Exercise 1, solutions here. I have yet to grade and return this assignment - you can pick it up between 10 and 2 on Monday, while I'm there. Any that are not picked up by then I'll put in the "Assignments for Waterman" folder on my bulletin board.
- You should be able to find eigenvalues and eigenvectors for 2x2 matrices. Assignment 13 Exercises 2 and 3, solutions here.
- You should know what it means to diagonalize a matrix, and you should be able to do it, given either of D = P-1AP or A = PDP-1. (You should also be able to get either of these from the other.) Assignment 14 Exercises 1 and 2, solutions here.
- You should be able to determine eigenvectors and eigenvalues for a given reflection or projection in R2. You should be able to use them and A = PDP-1 to determine the matrix of the transformation. Assignment 14 Exercises 1 and 2, solutions here, and 3/16 Class Exercise number 1, solution here.
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