Let P, 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) E P3. Is Da linear transformation? Let p(x) = a3x³3 + a2x² + a1x + ao and q(x) = bzx³ + b2x² + bịx + bo be any two polynomials in P3 and c e R. %3D a. D(p(x) + q(x)) = D(p(x)) + D(q(x)) = Does D(p(x) + q(æ)) = D(p(x)) + D(q(x)) for all p(x), q(x) E P3? b. D(cp(x)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c eR and all p(x) E P3? c. Is Da linear transformation?

Let P, 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) E P3. Is Da linear transformation? Let p(x) = a3x³3 + a2x² + a1x + ao and q(x) = bzx³ + b2x² + bịx + bo be any two polynomials in P3 and c e R. %3D a. D(p(x) + q(x)) = D(p(x)) + D(q(x)) = Does D(p(x) + q(æ)) = D(p(x)) + D(q(x)) for all p(x), q(x) E P3? b. D(cp(x)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c eR and all p(x) E P3? c. Is Da linear transformation?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 15EQ

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