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Let Pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D: P3 → P2 be the function that sends a polynomial to its derivative. That is, D(p(x)) = p'(x) for all polynomials p(x) P3. Is D a linear transformation? Let p(x) = a3x³ + a₂x² + α₁x + αº and q(x) = b3x³ + b₂x² + b₁x + b₁ be any two polynomials in P3 and c E R. a. D(p(x) + q(x)) = . (Enter a3 as a3, etc.) D(p(x)) + D(q(x)) = Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) = P3? choose b. D(cp(x)) = + c(D(p(x))) = î Does D(cp(x)) = c(D(p(x))) for all CER and all p(x) = P3? choose ◆ c. Is D a linear transformation? choose ◆

Let Pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D: P3 → P2 be the function that sends a polynomial to its derivative. That is, D(p(x)) = p'(x) for all polynomials p(x) P3. Is D a linear transformation? Let p(x) = a3x³ + a₂x² + α₁x + αº and q(x) = b3x³ + b₂x² + b₁x + b₁ be any two polynomials in P3 and c E R. a. D(p(x) + q(x)) = . (Enter a3 as a3, etc.) D(p(x)) + D(q(x)) = Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) = P3? choose b. D(cp(x)) = + c(D(p(x))) = î Does D(cp(x)) = c(D(p(x))) for all CER and all p(x) = P3? choose ◆ c. Is D a linear transformation? choose ◆

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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Let Pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D : P3 - P2 be the function that sends a polynomial to its derivative. That is, D(p(x)) = p' (x) for all polynomials p(x) = P3. Is D a linear transformation? Let p(x) = a³x³ + ²x² + a₁ + a₁ and q(x) = b3x³ + b₂x² + b₁x + b₁ be any two polynomials in P3 and c E R. a. D(p(x) + q(x)) = . (Enter a3 as a3, etc.) D(p(x)) + D(q(x)) = Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) = P3? choose b. D(cp(x)) = + c(D(p(x))) = = Does D(cp(x)) = c(D(p(x))) for all CER and all p(x) = P3? choose ✪ c. Is D a linear transformation? choose ◆
Transcribed Image Text:Let Pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D : P3 - P2 be the function that sends a polynomial to its derivative. That is, D(p(x)) = p' (x) for all polynomials p(x) = P3. Is D a linear transformation? Let p(x) = a³x³ + ²x² + a₁ + a₁ and q(x) = b3x³ + b₂x² + b₁x + b₁ be any two polynomials in P3 and c E R. a. D(p(x) + q(x)) = . (Enter a3 as a3, etc.) D(p(x)) + D(q(x)) = Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) = P3? choose b. D(cp(x)) = + c(D(p(x))) = = Does D(cp(x)) = c(D(p(x))) for all CER and all p(x) = P3? choose ✪ c. Is D a linear transformation? choose ◆
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