Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. let v be the vector space of all functions f : r ?

Let V be the vector space of all functions f : R ? R. Consider the...

50.1K

Verified Solution

Question

Advance Math

Let V be the vector space of all functions f : R ? R. Considerthe subspace W spanned by {sin(x), cos(x), e^x , e^?x}. Thefunction T : W ? W given by taking the derivative is a lineartransformation

a) B = {sin(x), cos(x), e^x , e^?x} is a basis for W. Find thematrix for T relative to B.

b)Find all the eigenvalues of the matrix you found in theprevious part and describe their eigenvectors. (One of the factorsof the characteristic polynomial will be ? 2+1. Just ignore thissince it has imaginary roots)

d) Use your answer to the previous part to find all theeigenvalues of T and describe their eigenvectors. Check that thefunctions you found are indeed eigenvectors of T.

Answer & Explanation Solved by verified expert
4.1 Ratings (604 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Medical Sciences
1.2K views

The lymphatic system includes our bodies' defenses against infections. AIDS, Leukemia, many autoimmune disorders, and allergies are...

Psychology
1.2K views

Identify the models of urban growth and explain how they differ. Why do these models tell...

Mechanical Engineering
1.2K views

Design a Turing Machine to construct the function f(n) = 4 [1/4 n] + 2, (that...

Civil Engineering
1.2K views

How we can determine the ESAL for the design period? Elaborate your answer with a numerical...

Accounting
1.2K views

Diaz Company issued $80,000 face value of bonds on January 1, 2018. The bonds had a...

Accounting
1.2K views

The company's DRAFT equity section reads, in part, as follows -...

Accounting
1.2K views

Under the step method of allocation, the total amount of service costs allocated...

Accounting
1.2K views

Entity F borrowed $60,000 on October 1, 2024 issuing a 6-month,10% interest-bearing note to the...

Accounting
1.2K views

First picture is the...

Accounting
1.2K views

D. LISP Inc. planea comprar un mezclador nuevo por $50,000. El nuevo equipo reemplazar una...

Finance
1.2K views

NTC company has an EM of 3.4 and JET Inc. has an EM of 2.5....

Accounting
1.2K views

what is the purpose of an entity relationship diagram? Should every entity in an entity...