Prove that the polynomials p₁(t)=2-t, p₂(t)=2+t, and p₁(t) = 8 are linearly dependent in P₂. Then find a basis for Span{p.(t), P₂(t),P3(t)}.
Prove that the polynomials p₁(t)=2-t, p₂(t)=2+t, and p₁(t) = 8 are linearly dependent in P₂. Then find a basis for Span{p.(t), P₂(t),P3(t)}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Prove that the polynomials p₁(t)=2—t, p₂(t)=2+t, and p²(t)=8 are
linearly dependent in P₂. Then find a basis for Span{ P₁(1), P₂(1),P3 (1)}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92856043-199e-49b6-95ce-27336f8d0cbd%2Fce3a33ad-921c-482c-a0e1-fc5a6a5ac110%2Fwih2f7_processed.png&w=3840&q=75)
Transcribed Image Text:Prove that the polynomials p₁(t)=2—t, p₂(t)=2+t, and p²(t)=8 are
linearly dependent in P₂. Then find a basis for Span{ P₁(1), P₂(1),P3 (1)}.
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