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Math Help - Finding invertible and diagonal matrix

  1. #1
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    Finding invertible and diagonal matrix

    Let A be a 3x3 Matrix (Im not sure how to make a matrix)

    A=
    -1 0 1
    5 3 2
    6 0 4

    Compute: An invertible Matrix P and diagonal matrix D such that AP=PD
    I am not sure what to do here, any help will be appreciated.
    Thanks!
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  2. #2
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    Re: Finding invertible and diagonal matrix

    Quote Originally Posted by farmeruser1 View Post
    Let A be a 3x3 Matrix (Im not sure how to make a matrix)

    A=
    -1 0 1
    5 3 2
    6 0 4
    [TEX]A=\left(\begin{matrix} -1 &0 &1\\5 &3 &2\\6 &0 4\end{matrix}\right)[/TEX] gives A=\left(\begin{matrix} -1 &0 &1\\5 &3 &2\\6 &0 &4\end{matrix}\right)
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  3. #3
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    Re: Finding invertible and diagonal matrix

    An n by n matrix is "diagonalizable" if and only if it has n independent eigenvectors. If that is true then "D" is the diagonal matrix having A's eigenvalues on its diagonal and "P" is the matrix whose columns are the corresponding eigenvectors (if eigenvalue [tex]\lambda[/itex] is at the first row, the first column of D is the eigenvector corresponding to \lambda, etc.
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