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Let P, denote the vector space of polynomials in the variable 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 P3. Is D a linear transformation? P Let p(x) = a3x³ + ₂x² + ₁ + aº and q(x) = b¸æ³ + b₂æ² + b₁ + b be any two polynomials in P3 and c E R. a. D(p(x) + g(x)) = D(p(x)) + D(q(x)) = + Does D(p(x) + q(x)) = D(p(x)) + D(g(x)) for all p(x), q(x) = P3? choose b. D(cp(r)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c ER and all p(x) = P3? choose c. Is D a linear transformation? choose (Enter a3 as a3, etc.)

Let P, denote the vector space of polynomials in the variable 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 P3. Is D a linear transformation? P Let p(x) = a3x³ + ₂x² + ₁ + aº and q(x) = b¸æ³ + b₂æ² + b₁ + b be any two polynomials in P3 and c E R. a. D(p(x) + g(x)) = D(p(x)) + D(q(x)) = + Does D(p(x) + q(x)) = D(p(x)) + D(g(x)) for all p(x), q(x) = P3? choose b. D(cp(r)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c ER and all p(x) = P3? choose c. Is D a linear transformation? choose (Enter a3 as a3, etc.)

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 ʼn 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 + ª₁x + ªº and q(x) = b3x³ + b₂x² + b₁x + bo be any two polynomials in P3 and c € R. a. D(p(x) + q(x)) : = 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(æ)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c € R and all p(x) = P3? choose c. Is D a linear transformation? choose (Enter a3 as a3, etc.)
Transcribed Image Text:Let Pn denote the vector space of polynomials in the variable x of degree ʼn 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 + ª₁x + ªº and q(x) = b3x³ + b₂x² + b₁x + bo be any two polynomials in P3 and c € R. a. D(p(x) + q(x)) : = 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(æ)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c € R and all p(x) = P3? choose c. Is D a linear transformation? choose (Enter a3 as a3, etc.)
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