Let P3 = {ao+a₁x + a₂x² + 3x³|ao, a₁, 02, 03 € R} be the vector space of polynomials of degrees at most 3 with real coefficients. Is {2, (5-x), (6+ x)², (8 − x)³} a basis of P3? Justify your answer.

Let P3 = {ao+a₁x + a₂x² + 3x³|ao, a₁, 02, 03 € R} be the vector space of polynomials of degrees at most 3 with real coefficients. Is {2, (5-x), (6+ x)², (8 − 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

Let P3 = {ao+a₁x + a₂x² +α3x³|ao, a₁, 02, 03 € R} be the vector space of
polynomials of degrees at most 3 with real coefficients. Is
{2, (5-x), (6+ x)², (8 - x)³}
a basis of P3? Justify your answer.

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