(2) Consider the space P2(R) of all polynomials of degree at most 2, equipped with the standard polynomial addition and scalar multiplication. Show that the set U₂ = {p(t) = a₁t + azt² a1, a2 € R} is a vector subspace of P₂(R).

(2) Consider the space P2(R) of all polynomials of degree at most 2, equipped with the standard polynomial addition and scalar multiplication. Show that the set U₂ = {p(t) = a₁t + azt² a1, a2 € R} is a vector subspace of P₂(R).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 11E

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Question

(2) Consider the space P2(R) of all polynomials of degree at most 2, equipped with
the standard polynomial addition and scalar multiplication.
Show that the set U₂ = {p(t) = a₁t + azt² a1, a2 € R} is a vector subspace
of P₂(R).

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