How can I accurately find eigenvalues for a Jordan canonical form matrix?

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The discussion focuses on accurately finding eigenvalues for a Jordan canonical form matrix, specifically the matrix | 1 1 1 |, |-1 -1 -1 |, | 1 1 0 |. The user initially calculated the eigenvalues incorrectly, obtaining λ3 = 4, while an online calculator provided the correct eigenvalues as λ3 = 0. The discrepancy arose from a sign error in the non-diagonal entries when applying the determinant formula det(A - xI) = 0.

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Homework Statement


Ok I was working with finding Jordan canonical form...
Here is the matrix I was working on:
| 1 1 1 |
|-1 -1 -1 |
| 1 1 0 |

I am having problem with finding eigenvalues... below is the attempt to solution
I was not getting the right answer. So, when I used online calculator to find the eigenvalue it was comletely different from what I got!

2. The attempt at a solution

|λ-1 , 1 , 1 |
|-1 , λ+1 , -1 |
|1 , 1 , λ |

So, I got values something λ3 = 4

The values from online calculator was λ3 = 0

Please help me in finding how they got eigenvalues all 0.
 
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You can either do det(A - xI) = 0, or det(xI - A) = 0, where A is your matrix and x I used instead of lambda. You chose to go with the second one. but forgot to change the signs of the non-diagonal entries.

Btw, I think this should go into "Calculus and Beyond". JCF certainly isn't precalculus material :P
 
oh sorry for wrong section, I am new to this forum...
 

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