Given a vector x Rn+l, the (n + l) Ã (n + l) matrix V defined by is called the Vandermonde matrix. (a) Show that if Vc = y and p(x) = c1 + c2x + ... + cn+1xn then p(xi) = yi, i = 1, 2, ..., n + 1 (b) Suppose that x1, x2,..., xn+1 are all distinct.

Given a vector x ˆˆ Rn+l, the (n + l) Ã— (n + l) matrix V defined by

is called the Vandermonde matrix.
(a) Show that if
Vc = y
and
p(x) = c1 + c2x + ... + cn+1xn
then
p(xi) = yi, i = 1, 2, ..., n + 1
(b) Suppose that x1, x2,..., xn+1 are all distinct. Show that if c is a solution to Vz = 0. Then the coefficients c1, c2,..., cn+1 must all be zero, and hence V must be nonsingular.