Let P₂ denote the vector space of polynomials of degree up to 2. Which of the following subsets of P₂ are subspaces of P₂? A. {p(t) |p(1) = 3} B. {p(t) | p' (8) = p(7)} c. {p(t) | p(−t) = p(t) for all t}

Let P₂ denote the vector space of polynomials of degree up to 2. Which of the following subsets of P₂ are subspaces of P₂? A. {p(t) |p(1) = 3} B. {p(t) | p' (8) = p(7)} c. {p(t) | p(−t) = p(t) for all t}

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

Let P₂ denote the vector space of polynomials of degree up to 2. Which of the following subsets of P₂ are subspaces of P₂?
A. {p(t) |p(1) = 3}
B. {p(t) | p' (8) = p(7)}
c. {p(t) | p(−t) = p(t) for all t}
D. {p(t) | p' (t) is constant}
Ē. {p(t) | p' (t) + 6p(t)+7=0}
OF. {p(t) |p(5)=0}

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A subset W of a vector space V is a subspace if and only if

1. $z e r o v e c t o r \vec{0} \in W$

2. $a u + b w \in W f o r a l l u, w \in W$

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