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May 26th, 2013, 05:07 AM   #1
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Eigenvector of 3x3 matrix

Hi,

I need to calculate the eigenvector of the following 3x3 matrix:
(3?2, 3, 0 | 0)
(3, 3?2, 3 | 0)
(0, 3, 3?2 | 0)

So I did several row operations and got this:
(?2, 1, 0 | 0)
(0, 1, ?2 | 0)
(0, 0, 0 | 0)

From which I got:
?2x + y = 0
y + ?2z = 0

I took y = constant and got:
?2x + y = 0 -> x = -y/?2
y + ?2z = 0 -> z = -y/?2

And got the eigenvector:
c (-1/?2, 1, -1/?2)

But my book says c (1, -?2, 1)? Does it matter that these results differ or does the constant term make them equal?
In other words: If I write my own result on a test, would I get any points? :P

Thanks for checking and advice!
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May 26th, 2013, 08:29 AM   #2
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Re: Eigenvector of 3x3 matrix

Your answer is fine, i'm assuming you know already that you can turn your answer into book's answer by having c absorb the factor



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May 30th, 2013, 08:51 AM   #3
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Re: Eigenvector of 3x3 matrix

What you wrote had me terribly confused! You say "find the eigenvector of this matrix". What you really mean is that you have already subtracted the eigenvalue from each diagonal term, writing as and that is the equation you are trying to solve.
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