? ? ? ? ? ✓ 1. V = C³ (R), and S is the subset of V consisting of those functions y satisfying the differential equation y"" + 3y x². ✓2. V = C¹(R), and S is the subset of V consisting of those functions f satisfying f'(0) > 0. 3. V R³, and S is the set of vectors (x1, x2, x3)T in V satisfying 1 5x₂ + x3 = 4. 4. V is the vector space of all real-valued functions defined on the interval [0, 1], and S is the subset of V consisting of those functions satisfying f(0) = ƒ(1). ✓5. V = C² (R), and S is the subset of V consisting of those functions satisfying the differential equation y" - 4y' + 3y = 0. Notation: Pr is the vector space of polynomials of degree up to n, and C" (R) is the vector space of n times continuously differentiable functions on R.
? ? ? ? ? ✓ 1. V = C³ (R), and S is the subset of V consisting of those functions y satisfying the differential equation y"" + 3y x². ✓2. V = C¹(R), and S is the subset of V consisting of those functions f satisfying f'(0) > 0. 3. V R³, and S is the set of vectors (x1, x2, x3)T in V satisfying 1 5x₂ + x3 = 4. 4. V is the vector space of all real-valued functions defined on the interval [0, 1], and S is the subset of V consisting of those functions satisfying f(0) = ƒ(1). ✓5. V = C² (R), and S is the subset of V consisting of those functions satisfying the differential equation y" - 4y' + 3y = 0. Notation: Pr is the vector space of polynomials of degree up to n, and C" (R) is the vector space of n times continuously differentiable functions on R.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Determine whether the given set SS is a subspace of the
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1. V = C³ (R), and S is the subset of V consisting of those functions y satisfying the differential equation y"" + 3y = x².
2. V = C¹ (R), and S is the subset of V consisting of those functions f satisfying f'(0) ≥ 0.
3. V = R³, and S is the set of vectors (x₁, x2, x3)T in V satisfying ₁ - 5x2 + x3 = 4.
4. V is the vector space of all real-valued functions defined on the interval [0, 1], and S is the subset of V consisting of those functions satisfying ƒ(0) = ƒ(1).
5. V = C² (R), and S is the subset of V consisting of those functions satisfying the differential equation y" — 4y' + 3y = 0.
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Notation: Pn is the vector space of polynomials of degree up to n, and C" (R) is the vector space of n times continuously differentiable functions on R.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d39a54-7451-4975-bf07-83fb2d3bea67%2F0bb07d72-4f50-43a4-9234-a56d63c5b5ee%2F8eyun2g_processed.png&w=3840&q=75)
Transcribed Image Text:?
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1. V = C³ (R), and S is the subset of V consisting of those functions y satisfying the differential equation y"" + 3y = x².
2. V = C¹ (R), and S is the subset of V consisting of those functions f satisfying f'(0) ≥ 0.
3. V = R³, and S is the set of vectors (x₁, x2, x3)T in V satisfying ₁ - 5x2 + x3 = 4.
4. V is the vector space of all real-valued functions defined on the interval [0, 1], and S is the subset of V consisting of those functions satisfying ƒ(0) = ƒ(1).
5. V = C² (R), and S is the subset of V consisting of those functions satisfying the differential equation y" — 4y' + 3y = 0.
-
Notation: Pn is the vector space of polynomials of degree up to n, and C" (R) is the vector space of n times continuously differentiable functions on R.
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