Problem 4Let V = P(R) and let L(V) be the vector space of all linear transformation on V. For j ≥ 1 defineT;(ƒ(x)) = f(i)(x), where ƒ(¹)(x) is the j-th derivative of f(x). Prove that the set {T₁, T2,...,‚Tn} is alinearly independent subset of L(V) for any positive integer n.

let n be any integer and a1,a2,...an be scalars such that a1T1+a2T2+a3T3+...+anTn=0 where T is the…

Answered: et V = P(R) and let L(V) be the vector…

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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et V = P(R) and let L(V) be the vector space of all linear transformation on V. For j ≥ 1 define ';(ƒ(x)) = f(i)(x), where ƒ(¹)(x) is the j-th derivative of f(x). Prove that the set {T₁, T₂,...,Tn} is a nearly independent subset of L(V) for any positive integer n.