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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?

1 Answers 1