Answered: 7.11. Let T: P₂ → R be a linear…

7.11. Let T: P₂ → R be a linear transformation and let p(x) = 1 + 2x, q(x) = 2 + 3x², r(x) = 1+x+x² and_s(x) = 7+16x. Given that T(p(x)) = 1, T(q(x)) = -2 and T(r(x)) = -1, compute T(s(x)).

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

Could you please help me by providing a matrix-based solution to this problem? I am struggling to find a solution using other methods and would appreciate your guidance. It would be very helpful if you could provide a step-by-step explanation using matrix notation exclusively.

Additionally, I have attached the question and answer for your reference. Could you please demonstrate the approach using matrices that leads to the solution?

7.11 Write s(x) as a linear combination of p(x), q(x), r(x). T(s(x)) = 3.

7.11. Let T: P₂ → R be a linear transformation and let
p(x) = 1 + 2x, q(x) = 2 + 3x², r(x) = 1 + x + x² and s(x) = 7+ 16x.
Given that T(p(x)) = 1, T(q(x)) = -2 and T(r(x)) = -1, compute T(s(x)).

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Step 1: Introduction

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Step 2: Write s(x) as a linear combination of p(x) , q(x) and r(x)

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Step 3: compute T(s(x))

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