  We study the linear algebra of finite subsets $S$ of a Segre variety $X$. In
particular we classify the pairs $(S,X)$ with $S$ linear dependent and
$\#(S)\le 5$. We consider an additional condition for linear dependent sets (no
two of their points are contained in a line of $X$) and get far better lower
bounds for $\#(S)$ in term of the dimension and number of the factors of $X$.
In this discussion and in the classification of the case $\#(S)= 5$, $X\cong
\mathbb {P}^1\times \mathbb {P}^1\times \mathbb {P}^1$ we use the rational
normal curves
