Math 311-200 - Test 2 Review
Date. Test 2 will be on Tuesday, 3/29/05. There is a practice
test on the web, Test 2, from
Fall 2004. Please bring an 8½×11 bluebook.
Extra office hours. I will have extra office hours on
Monday. For the Math 311-200 section, 12-1, and then for both
sections, 1-3.
Material covered.
-
Chapter 3, sections 3.1 through 3.6A in the text.
-
Methods
for Finding Bases.
-
Coordinate
Vectors and Examples
Calculators. The same rules we applied in Test 1 apply
here. Namely, you may use calculators to do arithmetic, although you
will not need them. You may not use any calculator that has
the capability of doing linear algebra or storing programs or other
material.
Problems. There will be 6 to 8 questions, some with multiple
parts. The questions will be similar to ones done for homework,
quizzes, or as examples in class or in the text. There will be one
``theory'' question taken from the following list.
- A question about linear splines similar to ones you have answered
on homework assignments.
- Be able to prove this representation theorem: If a vector
space V has a basis B = {v1, ...,
vn}, then every v in V can be uniquely
represented as
v = c1 v1 + ... + cn
vn, where the cj's are scalars.
- Be able to show that if a vector space V has a basis B =
{v1, ..., vn}, there every set
with n+1 or more vectors is linearly dependent.
- If A is an n×n matrix, show that the eigenvalues of A are
the roots of the characteristic polynomial,
pA(&lambda) = det(A - λ I).
Updated 3/26/05