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Given a 3x3 matrix

[tex]A = \[ \left[ \begin{array}{ccc} 0 & 0 & 1+2i \\ 0 & 5 & 0 \\ 1-2i & 0 & 4 \end{array} \right][/tex]

I need to a another 3x3 which satisfacies

D = U^-1 A U

Step 1.

Finding the eigenvalues

[tex]0 = det(A- \lambda I ) = (0- \lambda)(\lambda - 5) (\lambda -4 ), \lambda = 5,4,0[/tex]

step 2.

Finding the eigenvectors.

A vector which satisfies (A-\lambda I) v = 0

For \lambda = 5

p(\lambda = 5) = [tex] \[ \left[ \begin{array}{ccc} -5 & 0 & 1+2i \\ 0 & 0 & 0 \\ 1-2i & 0 & -1 \end{array} \right][/tex] ~ [tex]\[ \left[ \begin{array}{ccc} 1 & 0 & -1/5-2/5i \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right][/tex]

How do I read the eigenvector from the reduced matrix ???

Sincerely Fred

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# Homework Help: Eigenvalue and Eigenvector problem

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