2. Let P3(R) be the vector space of all polynomials of degree 3 or less (and the zero polynomial). Determine whether p(x) = x³ – 5x + 8 is in the subspace (S), where S = {67x* + x² + 9x + 4, 10x³ – 50x² + x + 6, 7x* + 23x² – x + 17}.
2. Let P3(R) be the vector space of all polynomials of degree 3 or less (and the zero polynomial). Determine whether p(x) = x³ – 5x + 8 is in the subspace (S), where S = {67x* + x² + 9x + 4, 10x³ – 50x² + x + 6, 7x* + 23x² – x + 17}.
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 10EQ
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Question
![2.
Let P3(IR) be the vector space of all polynomials of degree 3 or less (and the zero
polynomial). Determine whether p(x) = x³ – 5 + 8 is in the subspace (S), where
S = {67x* + x² + 9x + 4, 10x³ – 50x² + x + 6, 7x³ + 23x² – x + 17}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c5ad030-3ec8-4fd2-8d64-821b0d0d0877%2F4322b9e2-f317-4d39-bc28-b7ea4380770c%2Fir6laa5_processed.png&w=3840&q=75)
Transcribed Image Text:2.
Let P3(IR) be the vector space of all polynomials of degree 3 or less (and the zero
polynomial). Determine whether p(x) = x³ – 5 + 8 is in the subspace (S), where
S = {67x* + x² + 9x + 4, 10x³ – 50x² + x + 6, 7x³ + 23x² – x + 17}.
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