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Math Help - Eigenvectors

  1. #1
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    Eigenvectors

    I wasn't really sure where to put this but here seems the most appropriate place.

    I have to find eigenvectors corresponding to the eigenvalues of 0 1 and 4 for the following matrix:

    0 -8 4
    1 3 -1
    2 -2 2

    I have already found the eigenvevtors corresponding to 0 and 4, but when lamba =1 there is difficulty. Nothing seems to work when i try to equate the values. What is the way around this?

    By the way, when lamba=1, the result is as follows:

    -1 -8 4 = 0
    1 2 -1 = 0
    2 -3 1 = 0
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  2. #2
    Senior Member Dinkydoe's Avatar
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    What is the problem?

    You can simplify the system to:
    (By adding the last row to the middle-row)

    -x-8y+4z = 0
    3x = 0
    2x -2y+z = 0

    It follows that x = 0, and we can write the system as:

    x= 0,
    -8y+4z = 0
    -2y+z = 0

    Last 2 eqations are equivalent and we get: x=0, z = 2y so v=(0,1,2)
    Is an eigenvector by lambda= 1

    (I see in the last row you put a -3 for the second entry: this must be a -2)
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  3. #3
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    Thanks for spotting my mistake. The -3 is the reason i came into difficulty then. I shouldn't have any more problems now.
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