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Math Help - eigenvector

  1. #1
    Junior Member
    Joined
    Mar 2009
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    65

    eigenvector

    The matrix 1-2 25The matrix A = | 1 -2 |
    | 2 5 |
    has one eigenvalue of multiplicity 2. Find this eigenvalue and the corresponding eigenvector.

    I know the eigenvalue is 3 but i am not sure how you find the eigen vector, any help is appreciated.
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  2. #2
    Newbie
    Joined
    Mar 2010
    Posts
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    After you found the eigenvalue you must substitute the eignevalue into the formula:
    (eigenvalueI-A)X=0
    since the eigenvalue is 3 your matrix will look like:
    2,2
    -2,-2
    carry this matrix to reduced row echelon form:
    1,1
    0,0
    X is your eigenvector so the above matrix multiplied by X must equal 0. Say X is the column matrix = [a b] transposed. you get a=-b and b is arbitrary. Your eigenvector will then be:
    -1
    1
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