Multiplying the <Vandermonde matrix> $A_n$ by a coefficient vector $(c_0,\ldots,c_n)^T$ evaluates the <polynomial> $\sum_jc_jx^j$ at all nodes. If the result is zero, part (a)'s uniqueness for the zero interpolation data forces every coefficient to be zero. Thus the square <matrix> has trivial kernel and is invertible. Equivalently the interpolation map is a linear <bijection> between two spaces of <dimension> $n+1$.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / P / P3 / b / Solution

 Solution (source code)