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April 15th, 2010, 05:44 PM   #1
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Eigenvector Question

Suppose A is matrix such that det (A-hI)=h^2 - 6h + 9. Must there exist two linearly independent vectors b and c satisfying Ab=3b and Ac=3c?

I am stuck, I believe if we can show that the geometric and algebraic multiplicity are equal, then this is true. We know that the algebraic multiplicity will be =2 for eigenvalue of 3. However, how many eigenvectors are associated with this eigenvalue?
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April 17th, 2010, 01:01 AM   #2
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Re: Eigenvector Question

If you think it's not always true try to find a counter example. What about ?
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April 17th, 2010, 03:32 PM   #3
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Re: Eigenvector Question

Oh, ok then we would get an eigenvector of v1=t, v2=0 therefore we only have one eigenvector so the statement is false.
Thank you.
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