Eigenvalues of a 3x3 Matrix

  • Thread starter Jalo
  • Start date
  • #1
Jalo
120
0

Homework Statement


Given the matrix A=

1 -1 -1
-1 1 -1
-1 -1 1

Find the eigenvalues.


Homework Equations



I = identity matrix

The Attempt at a Solution



det(A-xI) = (1-x)3 - 2 - 3*(1-x) = 0 ⇔
⇔(1-x)3 - 3*(1-x) - 2 = 0

I can't find a way to solve this equation...
Any help would be appreciated!4

Daniel
 
Last edited by a moderator:

Answers and Replies

  • #2
Mentallic
Homework Helper
3,802
94
If you let y=1-x, then the cubic [itex]y^3-3y-2[/itex] has a zero at y=2.
 

Suggested for: Eigenvalues of a 3x3 Matrix

Replies
8
Views
597
  • Last Post
Replies
18
Views
1K
Replies
6
Views
254
  • Last Post
Replies
4
Views
871
Replies
9
Views
219
Replies
11
Views
264
Replies
4
Views
186
Replies
5
Views
1K
Top