Let P₂ denote the vector space of polynomials of degree up to 2. Which of the followingsubsets of P₂ are subspaces of P₂?A. {p(t) | p' (t) +8p(t) + 4 = 0}B. {p(t) | p(4) = 0}Oc. {p(t)p(t)dt = 0}D. {p(t) | p' (8) = p(2)}OE. {p(t) |p(-t) = p(t) for all t}OF. {p(t)|p(0) = 7}

Answered: Let P₂ denote the vector space of…

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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Recall that P₂(R) is the vector space of all polynomials of degree at most 2 with coefficients in R, with usual polynomial addition and scalar multiplication. For p = P₂(R), let p' denote the first derivative of p with respect to x. Show that U = {p(x) = P2(R) | p′(1) = p(0)} is a subspace of P₂(R).
The vector x is in a subspace H with a basis B = {b₁,b₂}. Find the B-coordinate vector of x. 1 -1. b₁ = 5 - 8 MG-18 [X] B b₂ - 1 |-*-[ X: 5 - 1
3. Let V = P3, the vector space of polynomials of degree at most 3. Let B {1, t, t², t³} and C = {t³,t,t², 1} be bases for P3. If f(t) = (1+ t)(t² + 4t + 1). Find [f(t)]8 and [f(t)]c
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' (t) is constant } B. {p(t) |p(-t) = -p(t) for all t} c. {p(t) | fp(t)dt = 0} D. {p(t) | p'(4) = p(0)} □E. {p(t) | p' (t) + 7p(t) + 5 = 0} F. {p(t) |p(8) = 3}
[1] 5. Let W be the subspace of R spanned by write j = |3| as the sum of a vector in W and a vector in
Let P2 denote the vector space of polynomials of degree up to 2. Which of the following subsets of P2 are subspaces of P2?
Let Pn be the vector space of polynomials of degree at most n and define L:P2 → P1 : p(t) → p'(t), p(t) e P2. (a) Show that L is linear. (b) Compute ker(L) and find dim(im(L)). (c) Is L is injective? Is L surjective? Justify your answers.
Which of the following subsets of P2 are subspaces of P2? OA. {p(t) | So p(t)dt = 0} ов. {p(t) | p'(€) + 9p(t) + 3 — 0} ос. (p(t) | p(0) — 7} {p(t) | p'(t) is constant } O E. {p(t) | p'(2) = p(1)} OF. {p(t) | p(4) = 0} O D.
q5
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Let P₂ denote the vector space of polynomials of degree up to 2. Which of the following absets of P₂ are subspaces of P2? A. {p(t) | p' (t) + 8p(t) + 4 = 0} B. {p(t) | p(4) = 0} c. {p(t)| Sop(t)dt = 0} D. {p(t) | p (8) = P(2)} E. {p(t) |p(-t) = p(t) for all t} OF. {p(t) |p(0) = 7}