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Problem. Recall that D = {1, t, t²,..., th} is a basis for Pn, and TD(x) = [x]D denotes the D-coordinate mapping. Let T: Pn → Pn denote the derivative (so, T(p) = p'). Both the domain and the codomain of the linear mapping F = T₂oToTp¹ are equal to Rn+1 and the mapping acts as follows: x → F(x) = T₂(T(Ãñ¹(x))). Find F(e;) for i = 1,..., n + 1. Find the standard matrix of this transformation when n = = 5.

Problem. Recall that D = {1, t, t²,..., th} is a basis for Pn, and TD(x) = [x]D denotes the D-coordinate mapping. Let T: Pn → Pn denote the derivative (so, T(p) = p'). Both the domain and the codomain of the linear mapping F = T₂oToTp¹ are equal to Rn+1 and the mapping acts as follows: x → F(x) = T₂(T(Ãñ¹(x))). Find F(e;) for i = 1,..., n + 1. Find the standard matrix of this transformation when n = = 5.

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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and Problem. Recall that D = {1, t, t²,..., t"} is a basis for P₁ TD(x) = [X] D denotes the D-coordinate mapping. Let T: Pn → Pn denote the derivative (so, T(p) = p'). Both the domain and the codomain of the linear mapping F = T₂ T T¹ are equal to R"+¹ and the mapping acts as follows: x → F(x) = TD (T(Ãñ¹(x))). Find F (e;) for i 1,..., n + 1. Find the standard matrix of this transformation when n = 5.
Transcribed Image Text:and Problem. Recall that D = {1, t, t²,..., t"} is a basis for P₁ TD(x) = [X] D denotes the D-coordinate mapping. Let T: Pn → Pn denote the derivative (so, T(p) = p'). Both the domain and the codomain of the linear mapping F = T₂ T T¹ are equal to R"+¹ and the mapping acts as follows: x → F(x) = TD (T(Ãñ¹(x))). Find F (e;) for i 1,..., n + 1. Find the standard matrix of this transformation when n = 5.
F(e)=To(T(Tr*(e:)))=To(T(*)) =To()=* F(е₂) = T₂(T(T5¹(ẹ₂))) = T(T(⋆)) = T₂(*) = ★ F(е3) = T₂(T(T5¹(ẹ3))) = TƊ(T(★)) = TD(*) = ★ F(е4) = T₂(T(T5¹(ẹ4))) = T(T(*)) = Tp(*) = ⋆ F(en+1)=To(T(T>*(en+1)))=To(T(*))=To(*)=*. enlace every instance of above with the correct quantity Delete
Transcribed Image Text:F(e)=To(T(Tr*(e:)))=To(T(*)) =To()=* F(е₂) = T₂(T(T5¹(ẹ₂))) = T(T(⋆)) = T₂(*) = ★ F(е3) = T₂(T(T5¹(ẹ3))) = TƊ(T(★)) = TD(*) = ★ F(е4) = T₂(T(T5¹(ẹ4))) = T(T(*)) = Tp(*) = ⋆ F(en+1)=To(T(T>*(en+1)))=To(T(*))=To(*)=*. enlace every instance of above with the correct quantity Delete
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