Let T be a linear transformation from P₂ to P₁ defined by the formulaT(a₁ + α₁x + a₂x²) = − 2xa₂ + ão - a₁.i. Find the matrix of T with respect to the bases: B₁ = {1 - x, x² + 2x − 1, 2x² + 2x + 1} of P₂and B₂ = {1- 2x, -1+x} of P₁.ii. Evaluate T(2x² − x+2) using the matrix of transformation T.

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Answered: Let T be a linear transformation from…

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 be a linear transformation from P₂ to P₁ defined by the formula T(ao + a₁x + a₂x²) = −2xa₂ + ao - α₁. i. Find the matrix of T with respect to the bases: B₁ = {1 − x, x² + 2x − 1, 2x² + 2x + 1} of P₂ and B₂ = {1-2x, −1+x} of P₁.