it has been a while I was not post in this forum

I need a little help with this one

First, let me defined the chebyshev system.

A linearly independent set of continuous functions \{u_0(x),u_1(x),\cdots, u_N(x)\} defined on [a,b] is a Chebyshev system if for any a\leq x_0<x_1<\cdots<x_N \leq b and y_0,\cdots,y_N \in \mathbb{R}, there is a unique linear combination u(x)=\sum_{j=0}^N{a_ju_j(x)} satisfying u(x_i)=y_i for i=0,\cdots,N

in \mathbb{R}, the set of N continuous functions consisting of the powers of x form a chebyshev system.

my question is why there is no Chebyshev system in \mathbb{R}^s for s \geq 2 ?

thanks for your comment
br