My Math Forum Eigenvector Question

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 April 15th, 2010, 04:44 PM #1 Senior Member   Joined: Sep 2009 Posts: 115 Thanks: 0 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?
 April 17th, 2010, 12:01 AM #2 Member   Joined: Nov 2009 From: France Posts: 98 Thanks: 0 Re: Eigenvector Question If you think it's not always true try to find a counter example. What about $A :=\begin{pmatrix}3&1\\0=&3\end{pmatrix}=$?
 April 17th, 2010, 02:32 PM #3 Senior Member   Joined: Sep 2009 Posts: 115 Thanks: 0 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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