How Do You Solve for Eigenvalues of This Specific 3x3 Matrix?

Jalo
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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:
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If you let y=1-x, then the cubic y^3-3y-2 has a zero at y=2.
 

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