Finding Eigenvalues with the Determinant Method

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Homework Help Overview

The discussion revolves around finding the eigenvalues and eigenvectors of a given 3x3 matrix using the determinant method. The original poster expresses confusion regarding the eigenvalues obtained through their calculations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use the determinant method to find eigenvalues but questions the validity of their result, suggesting a possible mistake or misunderstanding. Other participants inquire about the original poster's work and suggest reviewing the cofactor expansion method used.

Discussion Status

The discussion is ongoing, with participants providing feedback and prompting the original poster to clarify their calculations. There is no explicit consensus yet, but guidance has been offered regarding the method of cofactor expansion.

Contextual Notes

Participants are discussing the eigenvalue calculation method and the implications of the results, including the potential for missing eigenvalues. The original poster's initial result of only one eigenvalue raises questions about the completeness of their approach.

cscott
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Homework Statement



I need the eigenvalues and eigenvectors of [[0,0,1][0,2,0][1,0,0]]

The Attempt at a Solution



How come when I use the determinent method to get the eigenvalues I only end up with 2? Did I make a mistake or is there some other way I'm supposed to find -1, +1?
 
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If you mean what I think you mean, then you must have made a mistake. Can you show your work?
 
I used the cofactor expansion along the first row, like on wikipedia so the first two terms are zero and then for the last term: (1)det{ [[0, L-2][1, 0]] } = (0*0) - ((2-L)(1) => L-2 = 0 => L = 2
 
If you are expanding along the first row, there are two nonvanishing cofactors. There's an L in the first column and a 1 in the last.
 
Oops. Alright thanks.
 

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