Conditions for linear independence given the family of vectors is pairwise independent

Question

let $n>0, n \in \mathbb{N}$
Given $n+1$ vectors $a_0, a_1, ... a_n$ which are pairwise independent i.e. for all $i,j \in \{ 0,1,...,n \}$ and $i\neq j$, $a_i$ and $a_j$ are linearly independent. Under what conditions is $a_0, a_1, ... a_n$ a linearly independent family? This is of course not true in general. For eg: we can find infinitely many pairwise independent vectors in $\mathbb{R}^2$ but not more than 2 can form a linearly independent family.