...but any help is much appreciated!

Our aim is to find a polynomial of minimal degree passing through N

points Pi. All our constructions should depend on N.

The basic data is two matrices X:=matrix(1,N,[...]);

Y:=matrix(1,N,[...]), whose entries X[1,i] and Y[1,i] are the

coordinates of the point Pi, for 1 <= i <= N.

Assume that the the N points lie on the graph of the polynomial

T(X) = A1 + . . .ANX^(N−1). The coefficients Ai satisfy a system of

linear equations that can be written M.x = b where M and b depend

on the coordinates of the points Pi.

A. Write the matrix M as a function of the matrices X and Y .

B. Write the matrix b as a function of the matrices X and Y .

I have no idea. Please help!