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Let p(x) = α³x³ + α₂x² + α₁ x + α and q(x) = b3x³ + b₂x² + b₁x + bo be any two polynomials in 3 and c E R. a. D² (p(x) + q(x)) = D² (p(x)) + D²(q(x)) = Does D² (p(x) + q(x)) = D²(p(x)) + D² (q(x)) for all p(x), q(x) = ? choose b. D2(cp(x)) = + . c. Is D² a linear transformation? f is a linear transformation (Enter az as a3, etc.) c(D² (p(x))) = Does D²(cp(x)) = c(D² (p(x))) for all c ER and all p(x) E3? Yes, they are equal

Let p(x) = α³x³ + α₂x² + α₁ x + α and q(x) = b3x³ + b₂x² + b₁x + bo be any two polynomials in 3 and c E R. a. D² (p(x) + q(x)) = D² (p(x)) + D²(q(x)) = Does D² (p(x) + q(x)) = D²(p(x)) + D² (q(x)) for all p(x), q(x) = ? choose b. D2(cp(x)) = + . c. Is D² a linear transformation? f is a linear transformation (Enter az as a3, etc.) c(D² (p(x))) = Does D²(cp(x)) = c(D² (p(x))) for all c ER and all p(x) E3? Yes, they are equal

Advanced Engineering Mathematics
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 p(x) = α3x³ + ɑ₂ x² + α₁ x + ấ and q(x) = b3x³ + b₂x² + b₁x + bò be any two polynomials in O3 and c E R. a. D²(p(x) + q(x)) = D²(p(x)) + D²(q(x)) = Does D² (p(x) + q(x)) = D²(p(x)) + D²(q(x)) for all p(x), q(x) = ➡? choose b. D2(cp(x)) = + . (Enter az as a3, etc.) c(D² (p(x))) = Does D² (cp(x)) = c(D²(p(x))) for all c ER and all p(x) E? Yes, they are equal c. Is D² a linear transformation? f is a linear transformation
Transcribed Image Text:Let p(x) = α3x³ + ɑ₂ x² + α₁ x + ấ and q(x) = b3x³ + b₂x² + b₁x + bò be any two polynomials in O3 and c E R. a. D²(p(x) + q(x)) = D²(p(x)) + D²(q(x)) = Does D² (p(x) + q(x)) = D²(p(x)) + D²(q(x)) for all p(x), q(x) = ➡? choose b. D2(cp(x)) = + . (Enter az as a3, etc.) c(D² (p(x))) = Does D² (cp(x)) = c(D²(p(x))) for all c ER and all p(x) E? Yes, they are equal c. Is D² a linear transformation? f is a linear transformation
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