Let P(R) denote the vector space of polynomials with coefficients in R. Define 1. a function T: P(R) → P(R) by T(p)(x) = p(x) — p(0). a. Show that T is linear. b. Is T one-to-one? Either show it is one-to-one or illustrate by example that it is not. c. Is T onto? Either show it is onto or illustrate by example that it is not.

Let P(R) denote the vector space of polynomials with coefficients in R. Define 1. a function T: P(R) → P(R) by T(p)(x) = p(x) — p(0). a. Show that T is linear. b. Is T one-to-one? Either show it is one-to-one or illustrate by example that it is not. c. Is T onto? Either show it is onto or illustrate by example that it is not.

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 12EQ

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