8. Let P3(C) be a vector space over C and let D : P3(C) → P3(C) be thedifferential operator defined by D(p(t)) = dp/dt. Let p(t) = a+bt+ct² +dt³.Find the matrix of D relative to the basis {1,t, t², t³}.

D: P3ℂ→P3ℂ be the differential operatorDpt=dpdtrelative to the basis 1, t, t2, t3

Answered: 8. Let P3(C) be a vector space over C…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Find the matrix A' for T relative to the basis B'. T: R³- →→>>> R³, T(x, y, z) = A' = (x - y + 7z, 7x + y - z, x + 7y + z), B' = {(1, 0, 1), (0, 2, 2), (1, 2, 0)}
Let V be the vector space of functions spanned by B = {b₁ = 2 sin x + 9 cos x, b₂ = 4 sin x + 7 cos x} where x C = {C₁ = sin x, C₂ = cos } where x of coordinates matrix P. C+B P = C←B [f(x)] c = [ The coordinates of a function f(x) relative to the basis B are [f(x)] B = [8] 6 coordinates of f(x) relative to C and find f(x). f(x) = Ex: 3 Ex: 3 nn 2 sin x + -, ne Z nn 2,n € Z is also a basis for V. Find the change COS x Find the
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8. Let P3(C) be a vector space over C and let D: P3(C) → P3(C) be the differential operator defined by D(p(t)) = dp/dt. Let p(t) = a+bt+ct² +dt³. Find the matrix of D relative to the basis {1, t, ť², t³}.