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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let T be a linear transformation from P₂ to P₁ defined by the formula
T(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 P₂
and B₂ = {1- 2x, -1+x} of P₁.
ii. Evaluate T(2x² − x+2) using the matrix of transformation T.
Transcribed Image Text:Let T be a linear transformation from P₂ to P₁ defined by the formula T(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 P₂ and B₂ = {1- 2x, -1+x} of P₁. ii. Evaluate T(2x² − x+2) using the matrix of transformation T.
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