1. Let T: P2(R) → P2 (R) be the linear transformation given byT(f(x})) = x² f" (x) +2f'(x)Fix the following ordered bases of P2(R):A = {1, x, x²},= {1,1+x,1+x + x²}.%3DCompute [T]Ą.(b)Compute [T]g.(c)Find Q = [1P,(R)2, the change of coordinate matrix from Ato B. Use the change of coordinate formula and part (a) to confirm youranswer from part (b).

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1. Let T: P2(R) → P2(R) be the linear transformation given by T(f(x}) = x² f" (x) + 2f'(x) %3D Fix the following ordered bases of P2(R): A = {1, x, x²}, B = {1,1+x,1+ x +x²}. %3D |Compute [T]4. (b) Compute [T}g. (c) Find Q = [1B(R)]%, the change of coordinate matrix from A to B. Use the change of coordinate formula and part (a) to confirm your answer from part (b).

1. Let T: P2(R) → P2(R) be the linear transformation given by T(f(x}) = x² f" (x) + 2f'(x) %3D Fix the following ordered bases of P2(R): A = {1, x, x²}, B = {1,1+x,1+ x +x²}. %3D |Compute [T]4. (b) Compute [T}g. (c) Find Q = [1B(R)]%, the change of coordinate matrix from A to B. Use the change of coordinate formula and part (a) to confirm your answer from part (b).

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

1. Let T: P2(R) → P2 (R) be the linear transformation given by
T(f(x})) = x² f" (x) +2f'(x)
Fix the following ordered bases of P2(R):
A = {1, x, x²},
= {1,1+x,1+x + x²}.
%3D
Compute [T]Ą.
(b)
Compute [T]g.
(c)
Find Q = [1P,(R)2, the change of coordinate matrix from A
to B. Use the change of coordinate formula and part (a) to confirm your
answer from part (b).

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