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Math Help - I don't understand waht to do for diagonalization?

  1. #1
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    I don't understand waht to do for diagonalization?

    OK so on my homework it says Diagonalize the following matrix, if possible:

    [3 2 -2]
    [0 2 0]
    [0 1 3]

    I found out the eigenvalues which is 2 and 3. 3 is a repetition so that's why there's only 2.

    Now I'm suppose to find the eigenvalue. But I have no clue how to find the eigenvector. I'm readingm y textbook and the only thing that happens is they give me the eigenvalue then mysteriously find the eigenvector within one step.
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  2. #2
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    Re: I don't understand waht to do for diagonalization?

    If all else fails (or maybe it should cross your mind as an earlier choice), resort to the definitions.

    Your 3x3 matrix - A
    Your eigenvalue - 3
    An arbitrary column vector - [a\;b\;c]^{T} = x

    Ax = 3x

    Solve.
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  3. #3
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    Re: I don't understand waht to do for diagonalization?

    So I did Ax - 3x=0 and I got a row reduced 3x3 matrix with 2's as the diagonals Everything else are 0s... Is this suppose to be right?

    I'm sorry, but I'm just really bad at this stuff >.>. I'm not even sure if I can pass the class.
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