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Let the matrix $$ A = \begin{bmatrix} 40 & -29 & -11 \\ -18 & 30 & -12 \\ 26 & 24 & -50 \\ \end{bmatrix}$$ have a certain complex number $p \neq 0$ as an eigenvalue. Which of the following must also be an eigenvalue of $A$?

  1. $p+20$
  2. $p-20$
  3. $20-p$
  4. $-20-p$
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    Can you tell us why you cannot solve this? This should be quite standard.2012-11-30
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    @user32240 Also being an Indian, I can tell that this is a question from some competition and she wants be sure if her solution is correct.2012-11-30
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    Are those column vectors , row vectors?2012-11-30
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    @diimension I don't think it really matters in this context, the eigenvalues are invariant under transpose.2012-11-30
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    @EuYu I have much to learn :)2012-11-30
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    @diimension As do we all :)2012-11-30

2 Answers 2