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Consider the inner product space (P2, (, )) with the inner product (p(t), q(t)) = p(-1)q(-1)+p(0)q(0) +p(1)q(1). where p(t) and q(t) are in P2 If p(t) = 4+ 5t + 9t? and q(t) =1+4t, what is the orthogonal projection of p(t) onto q(t)?

Consider the inner product space (P2, (, )) with the inner product (p(t), q(t)) = p(-1)q(-1)+p(0)q(0) +p(1)q(1). where p(t) and q(t) are in P2 If p(t) = 4+ 5t + 9t? and q(t) =1+4t, what is the orthogonal projection of p(t) onto q(t)?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 12EQ
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Consider the inner product space (P2, (, )) with the inner product (p(t), q(t)) = p(-1)q(-1) +p(0)q(0)+ p(1)q(1). where p(t) and q(t) are in P2. If p(t) = 4+ 5t + 9t² and q(t) = 1+4t, what is the orthogonal projection of p(t) onto q(t)?
Transcribed Image Text:Consider the inner product space (P2, (, )) with the inner product (p(t), q(t)) = p(-1)q(-1) +p(0)q(0)+ p(1)q(1). where p(t) and q(t) are in P2. If p(t) = 4+ 5t + 9t² and q(t) = 1+4t, what is the orthogonal projection of p(t) onto q(t)?
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