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Math Help - Eigenvector problem

  1. #1
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    Eigenvector problem

    I need to determine Eigen vectors for the following matrix


    0 -1 4

    3 1 -1

    2 1 -2


    When I place the lambdas on diagonal row and calculate the Det A - Lambda I

    I am getting (-) lambda^3 - lamda^2 + 2 lamda = 0

    Therefore the only eigenvalue I get is lamda = 1

    Could someone please tell me if I am correct or not? Thanks Frostking
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  2. #2
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    Hi there

    Quote Originally Posted by Frostking View Post
    I need to determine Eigen vectors for the following matrix


    0 -1 4

    3 1 -1

    2 1 -2


    When I place the lambdas on diagonal row and calculate the Det A - Lambda I

    I am getting (-) lambda^3 - lamda^2 + 2 lamda = 0

    Therefore the only eigenvalue I get is lamda = 1

    Could someone please tell me if I am correct or not? Thanks Frostking

    This is wrong, first of all I got another determinant.

    And if you want to solve \lambda^3 - \lambda^2 + 2 \lambda  = 0
    then  \lambda = 0

    would be a solution too

    I had -lambda^3 - lambda^2+6lambda = 0 instead of your solution


    Hth
    Rapha
    Last edited by mr fantastic; October 31st 2009 at 10:51 PM. Reason: Fixed latex (\lambda not \lamda).
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  3. #3
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    Quote Originally Posted by Frostking View Post
    I need to determine Eigen vectors for the following matrix


    0 -1 4

    3 1 -1

    2 1 -2


    When I place the lambdas on diagonal row and calculate the Det A - Lambda I

    I am getting (-) lambda^3 - lamda^2 + 2 lamda = 0

    Therefore the only eigenvalue I get is lamda = 1

    Could someone please tell me if I am correct or not? Thanks Frostking
    Your characteristic equation is wrong. The red 2 should be a 6.

    There are 3 solutions. You should find them by first factorising the cubic.
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