Let Pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let r(x) E Pn be a fixed polynomial of degreen. Let f : P2 → Pn+2 be defined by f(p(x)) = p(x)r(x) for all polynomials p(x) E P2. Is f a linear transformation?Let p(x) = a2x2 + a1x + ao and q(x) = b2x² + b1x + bo be any two polynomials in P2 and c E R.a. f(p(x) +q(x)) =. (Enter az as a2, etc.)f(p(x)) + f(q(x)) =Does f(p(x) + q(x)) = f(p(x)) + f(q(x)) for all p(x), q(x) E P2? chooseb. f(cp(x)) =c(f(p(x)))Does f(cp(x)) = c(f(p(x))) for all cER and all p(x) E P2? choosec. Is f a linear transformation? choose

Introduction: A linear transformation is a function from one vector space to another that maintains…

Let Pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let r(x) E Pn be a fixed polynomial of degree n . Let f : P2 → Pn+2 be defined by f(p(x)) = p(x)r(x) for all polynomials p(x) E P2. Is ƒ a linear transformation? Let p(x) = a2x² + a1x + ao and q(x) = b2x? + b1x + bo be any two polynomials in P2 and c E R. a. f(p(x)+ q(x)) = (Enter az as a2, etc.) f(p(x)) + f(q(x)) = + Does f(p(x) + q(x)) = f(p(x)) + f(q(x)) for all p(x), q(x) E P2? choose b. f(cp(x)) = c(f(p(x))) = Does f(cp(x)) = c(f(p(x)) for all c E R and all p(x) E P2? choose c. Is fa linear transformation? choose

Let Pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let r(x) E Pn be a fixed polynomial of degree n . Let f : P2 → Pn+2 be defined by f(p(x)) = p(x)r(x) for all polynomials p(x) E P2. Is ƒ a linear transformation? Let p(x) = a2x² + a1x + ao and q(x) = b2x? + b1x + bo be any two polynomials in P2 and c E R. a. f(p(x)+ q(x)) = (Enter az as a2, etc.) f(p(x)) + f(q(x)) = + Does f(p(x) + q(x)) = f(p(x)) + f(q(x)) for all p(x), q(x) E P2? choose b. f(cp(x)) = c(f(p(x))) = Does f(cp(x)) = c(f(p(x)) for all c E R and all p(x) E P2? choose c. Is fa linear transformation? choose

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 4EQ

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