1. Which of the following must be true if A, a 2x2 matrix, has a nonzero eigenvector a satisfying Aa= 5a?
a) A's eigenvectors are all of R2
b) A must have at least an entire line through the origin in R2 as it's eigenvectors, where the vectors get stretched by 5.
c) A can have just the one eigenvector a that is stretched by 5.
d) A has two eigenvectors, the second being from Maple
e) none of the above

2. If the reduced augmented matrix for the system (A-lambdaI)x=0 is
Matrix([[0,0,0],[0,0,0]]),
with A as a 2x2 matrix
then the non-zero (real) eigenvectors of A are:
a) none
b) a line through the origin
c) all of R2
d) a subspace of R3 (with 3 coordinates)
e) none of the above

3. What are the non-zero real eigenvectors of
Matrix([[cos(Pi),-sin(Pi)],[sin(Pi),cos(Pi)]])?
a) none
b) a line of eigenvectors
c) two different lines of eigenvectors
d) all of R2
e) none of the above

4. If we write a basis for the eigenspace of
Matrix([[cos(Pi),-sin(Pi)],[sin(Pi),cos(Pi)]]), how many vectors does it have?
a) 0
b) 1
c) 2
d) infinite
e) none of the above

5. What are the non-zero real eigenvectors of
Matrix([[cos(Pi/5),-sin(Pi/5)],[sin(Pi/5),cos(Pi/5)]])?
a) none
b) a line of eigenvectors
c) two different lines of eigenvectors
d) all of R2
e) none of the above

Solutions
1. b)
2. c)
3. d)
4. c)
5. a)