Are There Integer Eigenvalues for a Specific Matrix?

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Homework Help Overview

The discussion revolves around finding the eigenvalues of the matrix [[3, -1], [-1, 1]]. The original poster is specifically interested in whether the eigenvalues can be integers.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to derive the characteristic polynomial and questions the correctness of their approach, noting the potential for non-integer eigenvalues. Other participants engage by affirming the correctness and questioning the complexity of further steps.

Discussion Status

The discussion includes affirmations of the original poster's approach, with some participants exploring the implications of non-integer eigenvalues and the complexity of the next steps without reaching a consensus.

Contextual Notes

Participants are considering the nature of eigenvalues and whether integer values are expected or necessary in this context.

cscott
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Homework Statement


I need the eigenvalues of [[3, -1][-1, 1]] (ie [[row1][row2]])

The Attempt at a Solution



A-xI = [[3-x, -1][-1, 1-x]]

so I get the characteristic polynomial x^2-4x+2=0 from det(A-xI)=0

Is this correct? Because I won't get integer eigenvalues from it
 
Last edited:
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Yeah, it is right.
 
Won't that be really messy to bring the matrix A-xI to RREF? (with x non-integer)
 
But in general, there is no reason why things have to be integer...
 
Thanks
 
Last edited:

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