I have matrix A(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \left(\begin{array}{ccc}6&2&-2\\-2&2&2\\2&2&2\end{array} \right) [/tex]

Its characteristic polynomial is

[tex]

p(\lambda)=\lambda^3 - 10\lambda^2 + 32\lambda -32

[/tex]

Finding minimal polynomial i get:

[tex] (I\lambda-A)^\vee=\left(\begin{array}{ccc}\lambda-6&-2&2\\2&\lambda-2&-2\\-2&-2&\lambda-2\end{array}\right)^\vee [/tex]

I cant understand why this last result equals with

[tex] \left(\begin{array}{ccc}\lambda^2-4\lambda&-2\lambda+8&2\lambda-8\\2\lambda-8&\lambda^2-8\lambda+16&2\lambda-8\\-2\lambda+8&2\lambda-8&\lambda^2-8\lambda+16\end{array} \right) [/tex]

can someone explain?

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# Minimal polynomial

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