Eigenvector of 3x3 matrix with complex eigenvalues

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SUMMARY

The discussion centers on the eigenvalues and eigenvectors of a 3x3 matrix A, specifically the matrix with elements 0, -6, 10; -2, 12, -20; and -1, 6, -10. The eigenvalues identified are 0, 1+i, and 1-i. However, it is concluded that 1+i and 1-i are not valid eigenvalues due to the resulting reduced row echelon form indicating no nonzero eigenvectors for these complex values. The correct approach to determining eigenvectors for complex eigenvalues is not addressed in the discussion.

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  • Understanding of eigenvalues and eigenvectors
  • Familiarity with reduced row echelon form (RREF)
  • Knowledge of complex numbers in linear algebra
  • Proficiency in matrix operations
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rayne1
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Matrix A:
0 -6 10
-2 12 -20
-1 6 -10

I got the eigenvalues of: 0, 1+i, and 1-i. I can find the eigenvector of the eigenvalue 0, but for the complex eigenvalues, I keep on getting the reduced row echelon form of:
1 0 0 | 0
0 1 0 | 0
0 0 1 | 0

So, how do I find the nonzero eigenvectors of the complex eigenvalues?
 
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rayne said:
Matrix A:
0 -6 10
-2 12 -20
-1 6 -10

I got the eigenvalues of: 0, 1+i, and 1-i. I can find the eigenvector of the eigenvalue 0, but for the complex eigenvalues, I keep on getting the reduced row echelon form of:
1 0 0 | 0
0 1 0 | 0
0 0 1 | 0

So, how do I find the nonzero eigenvectors of the complex eigenvalues?

Hi rayne!

It means that 1+i and 1-i are not actually eigenvalues.
How did you conclude they were?
 

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