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Math Help - Final today at 6 - Eigen Values in 3x3 matrix

  1. #1
    Junior Member
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    Final today at 6 - Eigen Values in 3x3 matrix

    | 1 2 0 |
    A = | 3 2 0 |
    | 0 0 3 |

    Find the eigen values and corresponding eigenspace. I know generally how to find eigenvalues but in a 3x3 matrix I get a cubic function that I cannot find the roots for. Thanks so much for the help!
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  2. #2
    Super Member Gamma's Avatar
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    solve det(A - Ix)=0

    I got det(A - Ix)=(3-x)[(1-x)(2-x)-2*3]=(3-x)[2-3x+x^2-6]=(3-x)(x-4)(x+1)

    so eigenvalues are 3,4,-1

    Can you take it from here? You just gotta solve:
    (A-I\lambda_i)v_i=0
    and these will give the the associated eigenvector to the eigenvalues.
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