We showed in class that B = {2-3x+x², 6-7x+x³} is a basis for the subspace U={p E R3[r]|p(1) = 0, p(2)=0}. (a) Extend B to a basis of R3[r]. (b) Find a subspace W such that R3[r] = UW. (c) Find the unique decomposition of h(x) = x³ - 2x² + 3x -3 determined by the direct sum [that is, write h(x) = u(x) +w(r), with u EU and w EW]

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