b) Solve L(fi) = 9; for the unknown polynomial fi in the following cases: i. 9₁ = X² + X³ ii. 92= 5X - X5 iii. 93 = 0
b) Solve L(fi) = 9; for the unknown polynomial fi in the following cases: i. 9₁ = X² + X³ ii. 92= 5X - X5 iii. 93 = 0
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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i need answers for part b and c only
![We denote the set of polynomials with real coefficients as
R[X] = {ao + a₁X + a₂X² +….. + anX": n ≤ N, ai ≤ R}.
Consider the map L : R[X] → R[X] defined as follows:
L(@+cX+cX? +...+cX”):=X+jaX? + jX® +.+,46Xn+
(a) Compute L(fi) for the following polynomials:
i. f₁ = 1+ X²
ii. f₂ = 1+X+X² + X³
iii. f3 = 5X + 4X² + 3X³ + 2X¹ + X5
(b) Solve L(fi) = 9; for the unknown polynomial f; in the following cases:
i. 9₁ = X² + X³
91
ii. 92 = 5X - X5
iii. 93 = 0
(c) Prove that L is a linear operator on R[X].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf62fff0-2315-44d2-8670-74ab8071a288%2F2d88aab9-fa94-4496-8bbd-cec9c98d00ab%2Fzgjfdq_processed.png&w=3840&q=75)
Transcribed Image Text:We denote the set of polynomials with real coefficients as
R[X] = {ao + a₁X + a₂X² +….. + anX": n ≤ N, ai ≤ R}.
Consider the map L : R[X] → R[X] defined as follows:
L(@+cX+cX? +...+cX”):=X+jaX? + jX® +.+,46Xn+
(a) Compute L(fi) for the following polynomials:
i. f₁ = 1+ X²
ii. f₂ = 1+X+X² + X³
iii. f3 = 5X + 4X² + 3X³ + 2X¹ + X5
(b) Solve L(fi) = 9; for the unknown polynomial f; in the following cases:
i. 9₁ = X² + X³
91
ii. 92 = 5X - X5
iii. 93 = 0
(c) Prove that L is a linear operator on R[X].
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