In each of the following, find the dimension of the subspace of P3 spanned by the given vectors:
(a) x, x − 1, x2 + 1
(b) x, x − 1, x2 + 1, x2 − 1
(c) x 2, x2 − x − 1, x + 1
(d) 2x, x − 2
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