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 (AhI)=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 ?

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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