I have given the following cone:
$P=\lbrace x | Ax \geq 0\rbrace$ where $A=\begin{pmatrix} -1& 1 & 0 & 0 & 0&0\\ 0& -1 & 1 & 0 & -1 & 0\\ 0 & 0 & -1 & 1 & 0 & 0\\ 0 & 0 & 0 & -1 & 1 & 1 \end{pmatrix}$. I am asked to find the extrem rays of this cone. Therefore, I first computed the rays of this cone, which are all vectors $d$ that satisfy $d\geq 0, Ad=0$. These are given by $d = \begin{pmatrix} \lambda \\ \lambda \\ \mu \\ \mu \\ \mu-\lambda \\ \lambda \end{pmatrix}$ with $\mu \geq \lambda \geq 0$. Now according to my lecture notes an extreme ray is defined as a ray in $P$ where $n-1$ linearly independent constraints are tight. In my case I have $6$ variables, so for an extreme ray $5$ constraints have to be tight. But I only have 4? So what does this mean? Did I make a mistake somewhere? Does this cone not have any extreme rays?