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Nullspace of a matrix

  1. Apr 15, 2009 #1
    Note: I don't know LaTeX that well, hence I have done my working in the images.

    1. The problem statement, all variables and given/known data

    Show that the rows of G are a basis for the null space of H (part of this question will be to show the independence explicitly).

    http://img.skitch.com/20090415-f6gewnam8bq6m971y9s7cam55q.preview.jpg
    Click for full size - Uploaded with plasq's Skitch

    2. Relevant equations

    Nullspace of H is the vector space of x, in which Hx=0. Basis is set of independent vectors that define this space.

    3. The attempt at a solution

    http://img.skitch.com/20090415-reqmbp49jacrhkme1886t1j5sx.jpg


    http://img.skitch.com/20090415-gwtu1hpgep9aun89isp16jxhwn.jpg

    Any help you can provide would be greatly appreciated.
     
  2. jcsd
  3. Apr 15, 2009 #2

    Dick

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    The rows of the vector G given in the problem statement are not in the nullspace of H. Your first attempt correctly identified a basis for the nullspace. The original problem is wrong.
     
  4. Apr 16, 2009 #3
    The question was right, elsewhere it mentioned that the work was in mod2.
     
  5. Apr 16, 2009 #4

    Dick

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    You REALLY should have said it was mod 2. Omitting that is actually criminal. There is no difference between -1 and +1 mod 2. Hence why are you complaining about sign changes?
     
  6. Apr 16, 2009 #5
    I was complaining when I did not realise I was working in mod 2. I only saw it was mod 2 after re-reading the question again and again.
     
  7. Apr 16, 2009 #6

    Dick

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    Ok, your complaint is shared. The question should have been more clearly stated.
     
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