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Problem. Consider the polynomials P1, P2, P3 P₁ defined by P₁(t) = 1+t P₂ (t) = 1-t ps(t) = 2. By inspection, write down a linear dependence relation among the three polynomials. Then find a basis for W = Span({P1, P2, P3}). Is it the case hat W = P₁? Explain your answer.

Problem. Consider the polynomials P1, P2, P3 P₁ defined by P₁(t) = 1+t P₂ (t) = 1-t ps(t) = 2. By inspection, write down a linear dependence relation among the three polynomials. Then find a basis for W = Span({P1, P2, P3}). Is it the case hat W = P₁? Explain your answer.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 54EQ
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Problem. Consider the polynomials P1, P2, P3 EP₁ defined by P₁(t) = 1+t P₂ (t) = 1 t P3(t) = 2. By inspection, write down a linear dependence relation among the three polynomials. Then find a basis for W = Span({P₁, P2, P3}). Is it the case that W = P₁? Explain your answer.
Transcribed Image Text:Problem. Consider the polynomials P1, P2, P3 EP₁ defined by P₁(t) = 1+t P₂ (t) = 1 t P3(t) = 2. By inspection, write down a linear dependence relation among the three polynomials. Then find a basis for W = Span({P₁, P2, P3}). Is it the case that W = P₁? Explain your answer.
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