This preview shows pages 1–2. Sign up to view the full content.
18.06 Problem Set 6
Due Wednesday, 9 April 2008 at 4 pm in 2106.
Problem 1:
a) Do problem 2 from section 6.1 (pg. 283) in the book.
b) Do problem 9 from section 6.1 (pg. 284).
Problem 2:
Do problem 13 from section 6.1 (pg. 285) in the book.
Problem 3:
Consider the matrix
M
=
2
2
1
1

14

6

9

7

2

1

2

1
8
1
7
4
a) One eigenvector is
x
1
= (1
,
1
,
0
,

3). What is the corresponding eigenvalue?
b) Note that det(
M
) = 0. Use this information to ﬁnd another eigenvalue
λ
2

how do you know this must be an eigenvalue?
c) A third eigenvalue is
λ
3
=

1. Write down (but don’t solve) a linear system
that can be solved to ﬁnd
x
3
.
d) What is the fourth eigenvalue? (Hint: use the trace.)
Problem 4:
a) Do problem 8 in section 6.2 (pg. 299)
b) Do problem 18 in section 6.2 (pg. 300)
Problem 5:
Here’s an example of an invertible 3 by 3 matrix with only 2 diﬀerent
eigenvalues:
A
=
4 1

1
2 5

2
1 1
2
a) Find the eigenvalues of
A
.
b) Find 3 linearly independent eigenvectors of
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 08/10/2008 for the course MATH 250 taught by Professor Chanillo during the Spring '08 term at Rutgers.
 Spring '08
 CHANILLO

Click to edit the document details