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For two polynomials p and q in P₂ let (p(q) = ₁² p (Note: the limits are unusual). Let U = Spann{P₁, P2} © P₂ where p₁ (t) = 1 and p₂(t) = t² p(t)q(t)dt. Determine the orthogonal projections of q(t) = t on U and U¹ Note: It is easy to miscalculate in this task so check your answers by making sure the answer you got makes sense

For two polynomials p and q in P₂ let (p(q) = ₁² p (Note: the limits are unusual). Let U = Spann{P₁, P2} © P₂ where p₁ (t) = 1 and p₂(t) = t² p(t)q(t)dt. Determine the orthogonal projections of q(t) = t on U and U¹ Note: It is easy to miscalculate in this task so check your answers by making sure the answer you got makes sense

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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For two polynomials p and q in P₂ let (p(q) = ₁² p (Note: the limits are unusual). Let U = Spann{P₁, P2} <P₂ where p₁ (t) = 1 and p₂(t) = p(t)q(t)dt. Determine the orthogonal projections of q(t) = t on U and U¹ Note: It is easy to miscalculate in this task so check your answers by making sure the answer you got makes sense
Transcribed Image Text:For two polynomials p and q in P₂ let (p(q) = ₁² p (Note: the limits are unusual). Let U = Spann{P₁, P2} <P₂ where p₁ (t) = 1 and p₂(t) = p(t)q(t)dt. Determine the orthogonal projections of q(t) = t on U and U¹ Note: It is easy to miscalculate in this task so check your answers by making sure the answer you got makes sense
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