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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
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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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}
Transcribed Image Text: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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Since you have posted a question with  multiple sub parts we will solve first three sub parts for you. To get remaining sub part solved please repost the complete question and mention the subparts to be solved

Solution

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

1. zero vector 0→ ∈W

2. au +bw∈ W for all u,w ∈W

 

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