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

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The discussion revolves around finding the eigenvalues of a given matrix to determine its Jordan canonical form. The user encountered discrepancies between their calculated eigenvalues and those produced by an online calculator. Their calculation led to an eigenvalue of λ3 = 4, while the online tool indicated λ3 = 0. It was noted that the user made an error by not changing the signs of the non-diagonal entries when applying the determinant formula. Clarification on the correct approach to calculating eigenvalues was requested, emphasizing the importance of proper matrix manipulation.
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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...
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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