1. Determine if the following sets are subspaces of the complex vector space P3(C). If the set is a subspace, you must use the subspace theorem to prove it. If the set is not a subspace, then you must provide a specific counter-example. (a) The set S = {p(x) = a + bx + bx² + (a+b)x³ | a,b ≤ C}. W = {p(x) = = a + bx + cx² + dx³ | a, b, c € C, d = R}. (b) The set

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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1. Determine if the following sets are subspaces of the complex vector space P3(C).
If the set is a subspace, you must use the subspace theorem to prove it. If the set is not a subspace,
then you must provide a specific counter-example.
(a) The set
S = {p(x) = a + bx + bx² + (a+b)x³ | a,b ≤ C}.
{p(x) = a +bx+cx² + dx³ | a, b, c = C, d ≤ R}.
(b) The set
W:
=
Transcribed Image Text:1. Determine if the following sets are subspaces of the complex vector space P3(C). If the set is a subspace, you must use the subspace theorem to prove it. If the set is not a subspace, then you must provide a specific counter-example. (a) The set S = {p(x) = a + bx + bx² + (a+b)x³ | a,b ≤ C}. {p(x) = a +bx+cx² + dx³ | a, b, c = C, d ≤ R}. (b) The set W: =
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