2. The set P3 of all polynomials of degree ≤ 3 with normal polynomial operations is a vector space. Which of the following are subspaces of P3 (a) U = {p(x) | p(x) ∈ P3, p(1) = 1} (b) U = {xq(x) : q(x) ∈ P3}

2. The set P3 of all polynomials of degree ≤ 3 with normal polynomial operations is a vector space. Which of the following are subspaces of P3 (a) U = {p(x) | p(x) ∈ P3, p(1) = 1} (b) U = {xq(x) : q(x) ∈ P3}

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 4EQ: In Exercises 1-4, let S be the collection of vectors in [xy]in2 that satisfy the given property. In...

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Question

2. The set P₃ of all polynomials of degree ≤ 3 with normal polynomial operations is a vector space. Which of the following are subspaces of P₃

(a) U = {p(x) | p(x) ∈ P₃, p(1) = 1}

(b) U = {xq(x) : q(x) ∈ P₃}

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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