Let V be the vector space of real-valued continuous functions on [0, 1] and let L : V → R be given by L ( f ) = f (0), for f in V .(a) Show that L is a linear transformation.(b) Describe the kernel of L and give examples of polynomials, quotients of polynomials, and trigonometric functions that belong to ker L .(c) If we redefine L by L ( f ) = f (1/2) , is it still a linear transformation? Explain.
Let V be the vector space of real-valued continuous functions on [0, 1] and let L : V → R be given by L ( f ) = f (0), for f in V .(a) Show that L is a linear transformation.(b) Describe the kernel of L and give examples of polynomials, quotients of polynomials, and trigonometric functions that belong to ker L .(c) If we redefine L by L ( f ) = f (1/2) , is it still a linear transformation? Explain.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section: Chapter Questions
Problem 16RQ
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Let V be the
(a) Show that L is a linear transformation.
(b) Describe the kernel of L and give examples of polynomials, quotients of polynomials, and trigonometric functions that belong to ker L .
(c) If we redefine L by L ( f ) = f (1/2) , is it still a linear transformation? Explain.
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