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October 30th, 2012, 11:14 AM   #1
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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!

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November 6th, 2012, 06:09 AM   #2
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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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