Nullspace of Matrix H: Proving Basis with Independent Rows

[Beam me down]

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[/color]

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.

 

[Dick]

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.

 

[Beam me down]

The question was right, elsewhere it mentioned that the work was in mod2.

 

[Dick]

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?

 

[Beam me down]

I was complaining when I did not realize I was working in mod 2. I only saw it was mod 2 after re-reading the question again and again.

 

[Dick]

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