R5, and S is the set of vectors (1, 2, 3) in V satisfying 2₁ - 7x2 + x3 6. the space of five-times differentiable functions R→ R, and S is the subset of V consisting of those functions satisfying the differential equation y(5) = 0. P3, and S is the subset of P3 consisting of all polynomials of the form p(x) = ax³ + bx. the space of three-times differentiable functions R→ R, and S is the subset of V consisting of those functions satisfying the differential equation y" + 5y = x². the vector space of all real-valued functions defined on the interval (-∞, ∞), and S is the subset of V consisting of those functions satisfying f(0) = 0. P5, and S is the subset of Ps consisting of those polynomials satisfying p(1) > p(0). R2, and S is the set of all vectors (1, ₂) in V satisfying 6x₁ + 7x₂ = 0.
R5, and S is the set of vectors (1, 2, 3) in V satisfying 2₁ - 7x2 + x3 6. the space of five-times differentiable functions R→ R, and S is the subset of V consisting of those functions satisfying the differential equation y(5) = 0. P3, and S is the subset of P3 consisting of all polynomials of the form p(x) = ax³ + bx. the space of three-times differentiable functions R→ R, and S is the subset of V consisting of those functions satisfying the differential equation y" + 5y = x². the vector space of all real-valued functions defined on the interval (-∞, ∞), and S is the subset of V consisting of those functions satisfying f(0) = 0. P5, and S is the subset of Ps consisting of those polynomials satisfying p(1) > p(0). R2, and S is the set of all vectors (1, ₂) in V satisfying 6x₁ + 7x₂ = 0.
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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Question
Transcribed Image Text:Determine whether the given set S is a subspace of the vector space V.
OA. V = R5, and S is the set of vectors (1, 2, 3) in V satisfying ₁ - 7x2 + x3 = 6.
OB. V is the space of five-times differentiable functions R → R, and S is the subset of V consisting of those functions satisfying the differential equation y(5) = 0.
OC. V = P3, and S is the subset of P3 consisting of all polynomials of the form p(x) = ax³ + bx.
OD. V is the space of three-times differentiable functions R → R, and S is the subset of V consisting of those functions satisfying the differential equation y" + 5y = x².
OE. V is the vector space of all real-valued functions defined on the interval (-∞, ∞), and S is the subset of V consisting of those functions satisfying f(0) = 0.
OF. V =
OG. V
P₁, and S is the subset of Ps consisting of those polynomials satisfying p(1) > p(0).
R2, and S is the set of all vectors (1, 2) in V satisfying 6x₁ + 7x₂ = 0.
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