# Nullspace of a matrix

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

Dick
Homework Helper
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.

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

Dick
Homework Helper
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?

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.

Dick