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Need Help On Eigenvalue and Eigenvector

Discussion in 'Mathematics and Physics' started by shermaine, Nov 27, 2006.

  1. shermaine

    shermaine New Member

    Joined:
    Jul 8, 2003
    Messages:
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    Hi Guys,

    I have got some enquires for eigenvalue and eigenvector.

    Consider the 1st matrix:

    A = [ 1 2 3]
    [ 0 5 6]
    [ 0 6 5]

    The characteristic polynomial is

    det(A-λI) = [ 1-λ 2 3]
    [ 0 5-λ 6]
    [ 0 6 5-λ]

    = (1-λ) [ (5-λ)^2 - 36]

    The eigenvaules are D(λ) = 0 ---> λ1 = 1, λ2=-1 and λ3 =11
    May i know how do we get the λ1 , λ2 and λ3? Can someone advise me?
    Dont seem quadratic is working for this??


    Matrix (2)

    A = [3 5 3]
    [0 4 6]
    [0 0 1]

    Is the characteristic polynomial: det(A - λI) = [ 3-λ 5 3]
    [ 0 4-λ 6]
    [ 0 0 1-λ]

    = (3-λ)[(4-λ)(1-λ)- 0]?


    Does the characteristic polynomial of matrix 2 also the same as Matrix (3)

    A = [ 3 0 0]
    [ 4 4 0]
    [ 5 6 1]

    Please advise. Thanks :)
     
  2. shermaine

    shermaine New Member

    Joined:
    Jul 8, 2003
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    how to get the attached circled?
     

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  3. Hayato

    Hayato Member

    Joined:
    Jun 21, 2006
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    BR
    Yes, they are the same.

    Just solve the det(A - λI).

    After you find the Eigenvalues, you need to find the Eigenvectors, by the method

    (A - λi*I)*Vi = 0, where i varies from 1 to n; If you have 3 eigenvalues, then n = 3...

    In the picture, you have a 3x3 matrix, so V is formed by 3 components (a,b,c) or (u,v,w)...
     
    Last edited: Nov 28, 2006

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