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decide whether each of the following sets is a subspace...

Question: decide whether each of the following sets is a subspace...

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Decide whether each of the following sets is a subspace of P. If it is, show that the set is non-empty and is closed under both addition and scalar multiplication. Otherwise, explain why the set is not a subspace of P. 1. (a) Bi-{p є P | p,(a)-0), where a is some fixed real number and p, denotes the derivative of p. (b) B2 = {p E P | p,(a) = 1), where a is some fixed real number. (c) B3 p EP is the zero polynomial (d) B IpE P P(0) > deg(p)), where deg(p) denotes the degree of p.

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