(a) Is the set S = {1 + x + x2, 1 − x3,  x + x2 + x3,  x3} ⊂ P3 linearly independent? If so, prove it. If not, give a subset of S which is linearly independent and has the same span as S. (b) Does S span P3? If so, prove it. If not, describe in words span S.

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