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Nullspace of a matrix

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

Homework Statement



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

Homework Equations



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

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.
 

Answers and Replies

  • #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.
 
  • #3
The question was right, elsewhere it mentioned that the work was in mod2.
 
  • #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?
 
  • #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.
 
  • #6
Dick
Science Advisor
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Ok, your complaint is shared. The question should have been more clearly stated.
 

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