3 2 Let P3 = {ax³ + bx² + cx + d | a, b, c, d = R} be the vector space of polynomials of degree at most 3. Le H = {pЄP3 | p(0) = 1}. Select ALL of the following statements that are true. His closed under addition. His closed under scalar multiplication. H is a subset of P3. H does not contain the zero polynomial. His a subspace of P3.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 39E
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Let P3 = {ax³ + bx² + cx + d | a, b, c, d = R} be the
vector space of polynomials of degree at most 3.
Le H = {pЄP3 | p(0) = 1}.
Select ALL of the following statements that are true.
His closed under addition.
His closed under scalar multiplication.
H is a subset of P3.
H does not contain the zero polynomial.
His a subspace of P3.
Transcribed Image Text:3 2 Let P3 = {ax³ + bx² + cx + d | a, b, c, d = R} be the vector space of polynomials of degree at most 3. Le H = {pЄP3 | p(0) = 1}. Select ALL of the following statements that are true. His closed under addition. His closed under scalar multiplication. H is a subset of P3. H does not contain the zero polynomial. His a subspace of P3.
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