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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3511a601-c894-498d-b22f-6f3b32960e8c%2F15ec311f-ba1c-4e36-97c3-1a8af2ef4598%2Fasjpg1k_processed.png&w=3840&q=75)
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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