In the context of a finite probability space, as in Theorem 2.1, show that the expected utility representation is determined up to a strictly positive linear transformation. 

Data From Theorem 2.1

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Theorem 2.1 Given the pair (M,R), if the preference relation R satisfies Assumptions 2.1-2.3, then there exist S scalars u(x) R, s = 1,..., S, such that, for every X1, X2 M, x R x2 U(x) > U(x2), (2.3)