Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

KatClaire

  • one year ago

Suppose A, B and X are invertible matrices such that BinverseXA = AB: Find an expression for X in terms of A and B.

  • This Question is Closed
  1. KatClaire
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[BX^{-1}A=AB\]

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

    I have a question to see if I'm doing this right. Do I first times each side by the inverse of B to get rid of it then by X??

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

    What does it mean that it is invertible

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

    determinant is not equal to zero

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

    Does that mean I can move them around any special way? I'm so confused

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

    say wuttt

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

    I still don't know how to do this :(

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

    is that from linear algebra class in college?

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

    yes

  10. joemath314159
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If the matrix A is invertible, that means there exists a matrix\[A^{-1}\]such that:\[AA^{-1}=A^{-1}A=I\]where I is the identity matrix.

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

    Okay I know that but I still want to know if what I wrote up there is on the right track

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

    yes, multiply both sides by \(B^{-1}\) and what do you get?

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

    you get \[x^{-1} A = B^{-1}AB\] so I went on and multiplied each side by X and then got \[A=XB^{-1}AB\] But I'm confused beacuse it doesn't look right

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

    I'm having a little trouble too actually :/ while I work on it, I can say that you can use \(AB=B^{-1}AB\) to make that a little prettier, but I still can't solve for \(X\) yet

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

    sorry my laptop decided to restart lol. So you're not allowed to rearrange the letters at all, right?

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

    or where did you get the B to? on the right side

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

    no, matrix multiplication is not commutative (cant move the letters)

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

    oh I see, I misread the question, sorry

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

    \[BX^{-1}A=AB\] all matrices are invertible solve for \(X\) correct?

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

    Yup!

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

    I tried switching them around in different ways but nothing works lol

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

    yeah, there must be some trick we're missing :/

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

    Like there's no way to rearrange it so that BA=AB ?

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

    only if BA and AB are inverses of each other, which I am trying to prove... so far unsuccessfully.

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

    I mean if A and B are inverses of each other, then AB=BA=I

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

    I think I'll just leave it and wait for the solution to be posted online to understand it lol thanks a lot for your help though!

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

    This will continue to bother me, please let me know the answer when you find out :) Sorry I couldn't really help.

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

    I really appreciate that you tried! I'll post the answer when it's up!

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

    Search OpenStudy
    • 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.