April 15th, 2010, 05:44 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, 01:01 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, 03:32 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. 

Tags 
eigenvector, question 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Eigenvector of 3x3 matrix  jones123  Calculus  2  May 30th, 2013 08:51 AM 
Orthogonal projection of eigenvector  Robertoo  Linear Algebra  3  January 5th, 2013 08:58 AM 
how to get the eigenvector and the corresponding eigenvalue  lakayii  Linear Algebra  2  September 24th, 2012 08:48 AM 
find eigenvector geometrically  mbradar2  Linear Algebra  5  March 18th, 2011 02:32 AM 
how to get the eigenvector and the corresponding eigenvalue  lakayii  Algebra  1  December 31st, 1969 04:00 PM 