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Math Help - Eigenspaces

  1. #1
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    Eigenspaces

    I needed to find the eigenvalues for the matrix
    5 0 1
    1 1 0
    -7 1 0

    Which I found to be 2 with multiplicity 3.

    Now I am required to find the eigenspace, and therein describe it geometrically.

    I believe that I am supposed to use this:

    det(2I-A)=0

    and then subsequently row reduce the augmented matrix to find the solution.
    I end up with an identity matrix with a column of zeroes, which would then mean that the matrix has only the trivial solution. Have I done this incorrectly? And if not, how do I describe this geometrically?
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  2. #2
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    You would like to find all \vec v such that

    A \vec v=2\vec v

    or equivalently

    (2I-A)\vec v=0.

    Now you should see that you need to find

    null(2I-A)

    and this is your eigenspace
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  3. #3
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    So should it be written as 0(2I-A) or as null(2I-A)?

    Because null equals zero?
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  4. #4
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    Nope, that is the null space. Have you dealt with null spaces before?
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  5. #5
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    No, I can't say I have. As a matter of fact, I haven't dealt with much of this linear algebra stuff at all. I am generally confused beyond... well... I'm so confused I don't even have an apt metaphor to describe it...
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  6. #6
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  7. #7
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    Thanks. I believe that we are going to be doing null spaces very shortly, as we are just starting to do linear transformations...
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