Let P, denote the vector space of polynomials in the variable of degree or less with real coefficients. Let D: P3 → P₂ be the function that sends a polynomial to its derivative. That is, D(p(z)) = p/(x) for all polynomials p(z) P3. Is D a linear transformation? Let p(x) = 3x³ + a₂z² + ª₁ + ª² and q(z) = b¸x³ + b₂x² + b₁z+bbe any two polynomials in P3 and c ER. a. D(p(z) +q(z)) = D(p(x)) + D(g(x)) = [ + Does D(p(z) + q(z)) = D(p(x)) + D(q(1)) for all p(x), g(x) = P3? choose b. D(cp(z)) = c(D(p(z))) = Does D(cp(z)) = c(D(p(z))) for all c R and all p(z) € P3? choose c. Is D a linear transformation? choose V (Enter as as a3, etc.)
Let P, denote the vector space of polynomials in the variable of degree or less with real coefficients. Let D: P3 → P₂ be the function that sends a polynomial to its derivative. That is, D(p(z)) = p/(x) for all polynomials p(z) P3. Is D a linear transformation? Let p(x) = 3x³ + a₂z² + ª₁ + ª² and q(z) = b¸x³ + b₂x² + b₁z+bbe any two polynomials in P3 and c ER. a. D(p(z) +q(z)) = D(p(x)) + D(g(x)) = [ + Does D(p(z) + q(z)) = D(p(x)) + D(q(1)) for all p(x), g(x) = P3? choose b. D(cp(z)) = c(D(p(z))) = Does D(cp(z)) = c(D(p(z))) for all c R and all p(z) € P3? choose c. Is D a linear transformation? choose V (Enter as as a3, etc.)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 65CR
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