Let Pn denote the vector space of polynomials in the variable a of degree n or less with real coefficients. Let D: P3 → P₂ be the function that sends a polynomial to itsderivative. That is, D(p(x)) = p'(x) for all polynomials p(x) = P3. Is D a linear transformation?Let p(x) = a³x³ + a₂x² + a₁x + a and q(x) = b3x³ + b₂x² + b₁ + bo be any two polynomials in P3 and c E R.a. D(p(x) + q(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? chooseb. D(cp(z)) =c(D(p(x))) =Does D(cp(x)) = c(D(p(x))) for all c ER and all p(x) = P3? choosec. Is D a linear transformation? choose(Enter a3 as a3, etc.)

Answered: Image /qna-images/answer/86a929eb-82c0-4b0b-bbae-737c4cba6b78.jpg

Let P, denote the vector space of polynomials in the variable a 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 +ao and q(x) = b3x³ + b₂x² + b₁ + b be any two polynomials in P3 and c E 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(z) € P3? choose b. D(cp(z)) = + c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all e 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 a 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 +ao and q(x) = b3x³ + b₂x² + b₁ + b be any two polynomials in P3 and c E 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(z) € P3? choose b. D(cp(z)) = + c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all e ER and all p(x) € P3? choose c. Is D a linear transformation? choose (Enter a3 as a3, etc.)

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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