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

The answer has been provided.Explanation:

Answered: (2) Consider the space P2(R) of all…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...

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(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).