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How do I go about solving this problem?

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- Apr 4th 2010, 05:29 PMtemaireEigenvalue
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How do I go about solving this problem? - Apr 4th 2010, 07:40 PMFancyMouse
1 is an eigenvalue of A means $\displaystyle det(A-I)=0$

So if we could try to get some value x such that $\displaystyle A^{2010}-2A+3I-xI$ can factor out an A-I, then we're done (using $\displaystyle det(MN)=det(M)det(N)$). Clearly x=2 works.