Correctness Given two arrays X and Y of n real numbers, the escalar product of X and Y is defined by

D = X[1]*Y[1] + X[2]*Y[2] + ... + X[n]*Y[n].

The following algorithm computes D:

EscalarProduct(X, Y)

D = 0

for i = 1 to n do

D = D + X[i] * Y[i]

return D

(a) State the appropriate loop invariant for the correctness of EscalarProduct.

(b) Show that your loop invariant from part (a) fulfills the underlying three properties and prove that EscalarProduct works correctly.