Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

LOOSEr

  • one year ago

what is a 3x3 invertible matrix?

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

    Are you OK with what a 3x3 matrix is?

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

    do you want a formal definition or a solved example showing all steps of inverting a 3x3 matrix?

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

    a solved example would be great

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

    ok

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

    @mathsmind ???

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

    which means its determinant cant be 0?

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

    yest i will show you the full steps

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

    consider the following matrix

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

    PLZ continue

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

    \[A=\left[\begin{matrix}1 & -2 & 0\\ 3& 1 & 5\\ -1 & 2 & 3\end{matrix}\right]\]

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

    Step one: \[A^T\]

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

    which means transpose of rows and columns of A

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

    \[A^T=\left[\begin{matrix}1 & 3 & -1\\ -2& 1 & 2\\ 0 & 5 & 3\end{matrix}\right]\]

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

    Step Two: find the adjoint or adjugate of A, which implies that we replace each element by their cofactor...

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

    If P = \begin{bmatrix} a &b &c \\ d &e &f \\ g &h &i \end{bmatrix}

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

    now please concentrate on this step it is simple but requires a bit of accuracy

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

    And P^4=2P how can we find P

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

    let's finish this first part then i will come to the 2nd question, you asked me first for a numerical example

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

    so we need to find adjA

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

    I know how to find a inverse matrix. So, can u plz do the 2nd question

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

    ok sure

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

    any idea?

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

    yes sorry am on the phone, but just a quick hint for P^n we use the principle of induction

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

    i will show you shortly

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

    @mathsmind ???

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

    @mathsmind why is taking so long?

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

    sorry back, am at work

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

    now P^4 means you are multiplying your matrix by itself 4 times.

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

    yep

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

    you know how to multiply the, it would be PP=P^2, then P^2P=P^3. then P^3P=P^4

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

    But it would be really long

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

    well this is the world of Matrices...

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

    are you thinking of algebraic operation on matrices such as taking the inverse of 2P

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

    or subtracting p^4-2P=0 in order to find the new P?

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

    Isn't there any short way

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

    have you done hermitian matrices...

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

    nope

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

    listen can we kindly finish this tonight because it is 5 am and i need to go ...

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

    okay

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

    i will provide you with full solution even if you are not online ok

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

    see ya tonight

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

    @ParthKohli

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

    lol, you still here? I thought you got help

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

    No

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

    can u do it?

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

    Short way

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

    I haven't done matrices yet: I am stuck with number theory at the moment.

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

    Nope.

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

    http://www.wikihow.com/Inverse-a-3X3-Matrix

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

    @looser there are many matrices such that P^4=2P but only one is invertible which is |dw:1361026643638:dw|

  51. 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.