, Let C" (R) be the vector space of "smooth" functions, i.e., real-valued functions f(x) in the variable z that have infinitely many derivatives at all points x E R. Let D : C" (R) →→ C®(R) and D2 : C¤(R) → C®(R) be the linear transformations defined by the first derivative D(f(x)) = f'(x) and the second derivative D²(f(x)) = f"(x). a. Determine whether the smooth function g(x) = 7e-lz is an eigenvector of D. If so, give the associated eigenvalue. If not, enter NONE. Eigenvalue = b. Determine whether the smooth function h(x) = sin(9x) is an eigenvector of D2. If so, give the associated eigenvalue. If not, enter NONE. Eigenvalue =

, Let C" (R) be the vector space of "smooth" functions, i.e., real-valued functions f(x) in the variable z that have infinitely many derivatives at all points x E R. Let D : C" (R) →→ C®(R) and D2 : C¤(R) → C®(R) be the linear transformations defined by the first derivative D(f(x)) = f'(x) and the second derivative D²(f(x)) = f"(x). a. Determine whether the smooth function g(x) = 7e-lz is an eigenvector of D. If so, give the associated eigenvalue. If not, enter NONE. Eigenvalue = b. Determine whether the smooth function h(x) = sin(9x) is an eigenvector of D2. If so, give the associated eigenvalue. If not, enter NONE. Eigenvalue =

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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