- #1
vabamyyr
- 66
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I have matrix A
[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 can't 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?
[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 can't 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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