Let $n \in \mathbb{N}$. We consider $n+1$ distinct points in $I$, denoted $x_0 < x_1 < \cdots < x_n$, and the polynomials $L_0, \ldots, L_n$ defined in Q5. Show that $(L_0, \ldots, L_n)$ is a basis of $\mathbb{R}_n[X]$.
Let $n \in \mathbb{N}$. We consider $n+1$ distinct points in $I$, denoted $x_0 < x_1 < \cdots < x_n$, and the polynomials $L_0, \ldots, L_n$ defined in Q5.
Show that $(L_0, \ldots, L_n)$ is a basis of $\mathbb{R}_n[X]$.