Problem 4: Let F be any field. Let P, be the space of F-coefficient polynomials of degree < n. Let To, ,I, be (n+1) distinct points in F. Show that for each set of (n+1) real numbers yo, · · , Yn: there exists a unique polynomial p(z) e P, which interpolates the points (ro, Yo), - · · , (In; Yn), i.e., p(r,) = y, for each i. ... %3D

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