5. Let P3 := {ª+a₁x+α₂x² + ª3x²³|ªo, ª1, a2, a3 ≤ R} be the vector space of polynomials of degrees at most 3 with real coefficients. Is {4, (3-x), (2+ x)², (1 − x)³} a basis of P3? Justify your answer.

5. Let P3 := {ª+a₁x+α₂x² + ª3x²³|ªo, ª1, a2, a3 ≤ R} be the vector space of polynomials of degrees at most 3 with real coefficients. Is {4, (3-x), (2+ x)², (1 − x)³} a basis of P3? Justify your answer.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 43E: Prove that in a given vector space V, the zero vector is unique.

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Question

5.
Let P3 = {ao+a₁x+ a₂x² + ª3x²³ |αo, 01, 02, 03 € R} be the vector space of
polynomials of degrees at most 3 with real coefficients. Is
{4, (3x), (2 + x)², (1 − x)³}
a basis of P3? Justify your answer.

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