Prove or disprove whether the transformations T defined below are linear.(i) Т(x1, х2, Xз) — (хз — х1 + 2х2, 0)(i) T(у) — У" +2y(iii) T(y)=|y(x)dx +1

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Prove or disprove whether the transformations T defined below are linear. (i) T(x1, X2, X3) = (x3 – X1 + 2x2, 0) (ii) T(y)=y" +2y (iii) T(y)= [ y(x)dx +1

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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Question

Prove or disprove whether the transformations T defined below are linear.
(i) Т(x1, х2, Xз) — (хз — х1 + 2х2, 0)
(i) T(у) — У" +2y
(iii) T(y)=|y(x)dx +1

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