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October 30th, 2012, 12:14 PM  #1 
Newbie Joined: Oct 2012 Posts: 15 Thanks: 0  Eigenvector of symmetric matrix
the vector (1 0 1)^t is an eigenvector of the symmetric matrix 6 1 3 1 7 x 3 x y how can i find x and y and the corresponding eigenvalue l.. I have no idea how to approach this question.. my understanding is that (1 0 1)^T is actually: 1 0 1 rows become columns and all that.. but how i can find the eigenvalue and original vector using this i dont know.. any help is appreciated! 
November 6th, 2012, 07:09 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Eigenvector of symmetric matrix
Do you not know what "eigenvalue" and "eigenvector" mean? A vector, v, is an eigenvector of linear transformation A, with eigenvalue , if and only if . I don't know what you mean by "the original vector". The is only one vector and it is given. Since we are told that is an eigenvector there must be a number such that . Multiplying out that left side, which gives the three equations , , and . That's pretty easy, isn't it? 

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eigenvector, matrix, symmetric 
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