Suppose that S is a vector space that is a subspace of the space of functions from R to R. Furthermore suppose that every element of S is a polynomial function, and that if p is in S then p(5)=k, where k is some constant. What must the value of k be equal to and why?

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 44EQ
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Suppose that S is a vector space that is a subspace of the space of functions from R to
R. Furthermore suppose that every element of S is a polynomial function, and that if p is
in S then p(5)=k, where k is some constant.
What must the value of k be equal to and why?
Transcribed Image Text:Suppose that S is a vector space that is a subspace of the space of functions from R to R. Furthermore suppose that every element of S is a polynomial function, and that if p is in S then p(5)=k, where k is some constant. What must the value of k be equal to and why?
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