Determine whether the following subset of P2 is a subspace of P2. {p(1): S p(t)dt :=0} Note: Pn is the set consisting of the zero polynomial combined with the set of all polynomials of degree less than or equal to n. Remember, to show that a subset IS a subspace you must show that for every f, g in the set and for every k E R we have that f + kg is also in the subset. To show that a subset is NOT a subspace you must either show that Ō is not in the subset or give specific ƒ and g in the set and k € R such that f+ kg is NOT in the subset.
Determine whether the following subset of P2 is a subspace of P2. {p(1): S p(t)dt :=0} Note: Pn is the set consisting of the zero polynomial combined with the set of all polynomials of degree less than or equal to n. Remember, to show that a subset IS a subspace you must show that for every f, g in the set and for every k E R we have that f + kg is also in the subset. To show that a subset is NOT a subspace you must either show that Ō is not in the subset or give specific ƒ and g in the set and k € R such that f+ kg is NOT in the subset.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Determine whether the following subset of P₂ is a subspace of P2.
1
{p(t): ["'p(t)dt = 0}
S
Note: P is the set consisting of the zero polynomial combined with the set of all polynomials of degree
less than or equal to n.
Remember, to show that a subset IS a subspace you must show that for every f, g in the set and for
every k ER we have that f + kg is also in the subset. To show that a subset is NOT a subspace you
must either show that is not in the subset or give specific f and g in the set and k € R such that
f + kg is NOT in the subset.
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