Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

thdrbird

  • one year ago

Let A = [-3,2,6 0,-1,6 0,0,-3] Find an invertible matrix P and a diagonal matrix D such that D = P^{-1}AP. find P and D I worked out the polynomial -7x^3-7x^2-15x-9 to give x= -1,-3,-3 My answer for P= [1,0,0 1,-3,-3 0,1,1] and D= -1,0,0 0,-3,0 0,0,-3 something's wrong!

  • This Question is Open
  1. electrokid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    what type of decomposition are you doing here ?

  2. Hoa
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think you get something wrong at P, since eigenvalue -3 has 2 dimensions and they are not yours! recheck

  3. electrokid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you should get D=dia(-3,-1,-3)

  4. Hoa
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, surely, because they are eigenvalues of A, what I need is checking the order this guy arrange in P to have corresponding of numbers, like (-3,-1,-3) or (-1,-3,-3)

  5. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok I will try!

  6. Hoa
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We cannot guess, right, kid? if we mess the order up, although we know it is the Diagonal matrix of A but the P is in different order of eigenvectors, We will be crazy when checking what wrong is, I had that experience. It made me crazy

  7. electrokid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    tr(A)=-3-1-3=-7 A11+A22+A33=3+9+3=15 |A|=-3(3)=-9 so, the characteristic polynomial would be\[\Delta(t)=t^3+7t^2+15t+9\]

  8. electrokid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    well, as long as the eigen vector columns are arranged in proper order, you should be good.

  9. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    still no luck...

  10. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no

  11. electrokid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    eigen vectors=? for t=-1: \[-2x+2y+6z=0\\6z=0\\-3z=0\implies v_1=(1,1,0)^T\]

  12. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yup

  13. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and v2 and v3 I put at (0,-3,1)

  14. electrokid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    for t= -3: \[ 2y+6z=0\\ 2y+6z=0\\ v_{2,3}=(\alpha,-3\beta,\beta)^T \]

  15. electrokid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @thdrbird you cannot have them two identical

  16. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh,ok..

  17. electrokid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you can use v2 when a=0,b=1 v3 when a=1,b=1

  18. electrokid
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    or v3 when a=1,b=0 ANY combination of alpha and beta that do not give the same vectors..

  19. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can you give me an example?

  20. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    got it!

  21. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I forgot to set alpha!

  22. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks @electrokid, great help!

  23. thdrbird
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Hoa as well! Thanks!

  24. Hoa
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I did nothing guy!!!

  25. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.