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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer question 1c
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 Tonto? Either show it is onto or illustrate by example that it is not.
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