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Math Help - Eigen Vector

  1. #1
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    Eigen Vector

    EDIT: just writing out my working. 2 mins .

    http://www.wolframalpha.com/input/?i=eigenvalues+{{1%2C+1%2C+1}%2C{2%2C2%2C+2}%2C+{3 %2C+3%2C+3}}

    How is {1, 2, 3} and answer(Corresponding to EV = 6)? I get {2, 1, 0) and just can't seem to work out how they get (1, 2, 3)!

    Eigen Value 6:

    \begin{matrix}5 & -1 & -1 \\ -2 & 4 & -2 \\ -3 & 3 & -3 \end{matrix}

    So, for
    -3x -3y + 3z = 0
    x + y  - z = 0
    I obtain:
    y\vec{-1, 1, 0) + z\vec{1, 0 , 1)

    -2x -4y + -2z = 0
    x  -2y  + z = 0
    I obtain:
    y\vec{2, 1, 0) + z\vec{-1, 0 , 1)


    ...And actually just typing this out i've mega confused myself as there are now 4 different basis and there's meant to be a max of 3 :S.
    Last edited by AshleyT; August 18th 2011 at 01:38 AM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Eigen Vector

    The matrix is A=\begin{bmatrix}{1}&{1}&{1}\\{2}&{2}&{2}\\{3}&{3}  &{3}\end{bmatrix} so, \ker (A-6I) \equiv\begin{Bmatrix}-5x_1+x_2+x_3=0\\2x_1-4x_2+2x_3=0\\3x_1+3x_2-3x_3=0\end{matrix} . Verify that (1,2,3) is a solution and (-2,1,0) it is not.
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  3. #3
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    Re: Eigen Vector

    EDIT: Just realised i massive stupid mistake in calculating all of these! Nvm.

    Thankyou!
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