Math 308 G Final
WHEN: Monday June 4th
WHERE: 2:30-4:20 in RAI 116
RULES: One single-sided page of hand-written notes is allowed. No calculators.
Material covered:
- The test will be cumulative with heavy emphasis placed on Chapter 4 sections 4.1, 4.2, 4.3, 4.4, 4.5, 4.7 and 4.8.
- There will be eight problems, Problem 8 is extra credit.
- YOU NEED TO KNOW:
- Be able to solve the eigenvaule problem for a 3 by 3 matrix
- Be able to find a basis for the range of a matrix which consists of columns of the matrix
- Know how to produce an orthonormal basis
- For the conceptual problem know how to prove the three properties of orthogonal matrices given in the book (we covered them in class also)
- There will be five true-false: be comfortable with similarity and eigenvalues
- Know when a matrix is diagonalizable
- Know least squares and data fitting
- Be able to solve a 2 by 2 system of differential equations
- Be able to find the exponential of a diagonalizable matrix.
Study Resources:
- Office hours: I will hold office hours from 12:00-2:00 before the Final Monday June 4th. Also feel free to arrange to meet with me at another time.
- We will review in class on Friday
- Problems from your book which are (VERY) representative of those on the Final:
- § 1.8 #1, 2, 3, 4
- § 3.4 #11, 12, 13, 14, 15, 16
- § 3.6 #19, 20
- § 3.8 #7, 8, 9, 10
- § 4.5 #4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17
- § 4.7 #1-12 (for 1-6 if the matrix is diagonalizable compute its exponential), 28, 43
- § 4.8 #15, 16
- Finals from past classes to practice on:
- The final, with solutions, from a 308 class taught by John Palmieri
- A final from a class taught winter quarter 2006. This one does not have solutions and is not very representative of the final I will be giving.
Results,
Stats: Average: 73 ; Median: 74 ; High Score: 107
Comments
- Problem 1: This one is just like the one you saw on quiz three except for the exponential bit at the end. Most people scored well
- Problem 2: Again most people did well, mostly computational errors when they occured
- Problem 3: Part (a): We saw that this is false on the last quiz: it's posted on the quiz page; Part (b): The stipulation that the matrix has real eigenvalues is a red herring: any matrix is similar to an upper triangular. However since we only briefly mentioned this in class and our emphasis was on the real case I felt that this problem was too tricky and gave everyone credit; Part (c) This was one of the review problems given above; Part (d) This we covered in class; Part (e) Problem 5 (a) is a counter-example
- Problem 4: Was tough on the grading of this one because I made it clear that something like this was going to be on the test
- Problem 5: The only funny one is (e), but of course the zero matrix is already diagonalized so certainly it's diagonalizable
- Problem 6: Full credit for most people here
- Problem 7: Again most people got this one
- Problem 8: Nobody got this one exactly but several came close; here we can use the formula for the exponential since the given matrix is nilpotent.
I'm heading out of town so if you would like to pick up you exam contact me after June 17th. You may inquire via email about your grade though I cannot promise speedy response.
Class Grades: The Median was placed at 2.9.
--FINAL--
Solutions