Let \( T: P_2 \rightarrow P_2 \) be a function represented by\[ T(c + bx + ax^2) = (3c + a) + (2b + 3a)x + ax^2 \]Determine whether \( T \) is a linear transformation.

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Answered: Let T : P2 → P2 be a function…

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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Let T : P2 → P2 be a function represented by T(c+ bx + ax?) = (3c+ a) + (2b + 3a)a + ax? Determine whether T is a linear transformation.