## Solution for problem 15 Chapter 6.1

# a. Let V = C1(I) be the vector space of continuously differentiable functions on the

Linear Algebra: A Geometric Approach | 2nd Edition

a. Let V = C1(I) be the vector space of continuously differentiable functions on the open interval I = (0, 1). Define T : V V by T (f )(t) = tf _ (t). Prove that every real number is an eigenvalue of T and find the corresponding eigenvectors. b. Let V = {f C0(R) : limt f (t)|t |n = 0 for all positive integers n}. (Why is V a vector space?) Define T : V V by T (f )(t) = _ t f (s)ds. (If f V , why is T (f) V ?) Find the eigenvalues and eigenvectors of T .

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The given vectors are and .

Find the dot product of both the given vectors.

###### Chapter 6.1, Problem 15 is Solved

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a. Let V = C1(I) be the vector space of continuously differentiable functions on the