ma253
, Fall
2007
— Problem Set Last
This is a
big
assignment. The theory of eigenvalues and eigenvectors is
critical and will be the main focus of the final exam. In order find eigenval
ues, you need to understand determinants at least a little bit. This assign
ment tries to get you to really think about both things. Let’s make it due on
the last day of classes,
Friday, December 7
.
1.
Problems from the textbook:
a. Section
6
.
1
, problems *
26
,
28
, *
30
, *
32
, *
44
.
b. Section
6
.
2
, problems *
4
, *
6
(do these two by hand), *
14
, *
16
, *
18
,
*
30
,
50
(the last one is very hard).
c. Section
7
.
1
, problems
1
–
5
, *
6
, *
8
,
15
–
19
,
33
, *
36
.
d. Section
7
.
2
, problems
1
–
7
, *
8
, *
10
, *
12
,
15
, *
16
, *
28
, *
33
, *
38
.
e. Section
7
.
3
, problems
1
–
5
, *
6
,
7
–
9
, *
10
, *
14
, *
18
,
35
,
36
,
48
.
f. Section
7
.
4
, problems
1
–
8
, *
10
, *
12
, *
18
.
*2.
Suppose
v
is an eigenvector of an invertible
n
×
n
matrix
A
, correspond
ing to an eigenvalue
λ
. Let
I
be the identity matrix.
a. Is
v
an eigenvector of
A
3
? If so, what is the eigenvalue?
b. Is
v
an eigenvector of
A

1
? If so, what is the eigenvalue?