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c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in part b.

c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in part b.

Advanced Engineering Mathematics
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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b. Prove that the polynomials form a basis for P₂. P₁(t)=1, p₂ (t)=1-t, and p₂ (t)=1+t-t²,
Transcribed Image Text:b. Prove that the polynomials form a basis for P₂. P₁(t)=1, p₂ (t)=1-t, and p₂ (t)=1+t-t²,
c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in part b.
Transcribed Image Text:c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in part b.
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