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    Orthogonal Matrix : Diagonalizability

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    Dtermine whether or not the following matrix
    A= 5 0 2
    0 5 0
    2 0 5
    is diagonalizable. If it is, then determine
    P'-1(P inverse)AP.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:54 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/orthogonal-matrix-diagonalizability-17861

    Solution Preview

    If a matrix is diagonalizable, then the matrix will have n ( or in this case 3) independent eigenvalues:

    Set up the equation: det(A-rI) = 0 to get the characteristic equations:

    | 5-r 0 2 |
    | 0 5-r 0 | = 0
    | 2 0 5-r|

    (5-r)^3 - 4(5-r) = 0
    (5-r)[(5-r)^2 - 4] = 0

    Thus ...

    Solution Summary

    Eigenvlaues, determinants and inverses are used to determine the diagonlizability of a given matrix.

    $2.49

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