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
Section6.4: Linear Transformations
Problem 24EQ
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![1.
Let P(R) denote the vector space of polynomials with coefficients in R. Define
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01b4eff1-1c92-4d86-9563-264f29556131%2Fa4080af0-8608-492f-96b5-be82c9841567%2Ffdc3b2a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
Let P(R) denote the vector space of polynomials with coefficients in R. Define
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.
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