I want to find the kernel basis of the transformation matrix:
\begin{pmatrix} 1 & -1 & 1 & -1\\ 1 & 0 & 0 & 0\\ 1 & 1 & 1 & 1\\ \end{pmatrix}
I have reduced the matrix to :
\begin{pmatrix} 1 & 0 & 0 & 0\\ 0 & 1 & 1 & 1\\ 0 & 0 & 1 & 0\\ \end{pmatrix}
I see we have one free variable (x4). How do I go on from here?