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Math Help - One More Lin Alg

  1. #1
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    One More Lin Alg

    Find a 3x3 matrix A which has the following eigenvalues and corresponding eigenvectors, respectively:

    Eigenvalues: 0, 1, -1

    Eigenvectors: [0,1,-1], [1,-1,1], [0,1,1]

    (So eigenvalue 0 corresponds to the eigenvector [0,1,-1], etc.).
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  2. #2
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    Quote Originally Posted by caeder012 View Post
    Find a 3x3 matrix A which has the following eigenvalues and corresponding eigenvectors, respectively:

    Eigenvalues: 0, 1, -1

    Eigenvectors: [0,1,-1], [1,-1,1], [0,1,1]

    (So eigenvalue 0 corresponds to the eigenvector [0,1,-1], etc.).
    If you create a coloum matrix of eigenvectors and call it M. Then if M is invertible we will have that MXM^{-1} = D where D is a diagnol matrix whose entries are the eigenvalues. So X = M^{-1}DM. And that is your matrix.
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