Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

liliy Group Title

Show that if A is nxn and has all 0’s on and below the diagonal then An = 0. Hint: do not at first be too ambitious. First find A2 and observe something useful about it. What about A3?

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    What is An?

    • 2 years ago
  2. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the matrix

    • 2 years ago
  3. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    commonly seen as Ax=b. this is An=0.

    • 2 years ago
  4. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh I thought there might have been a difference because you called the matrix A then you called it An

    • 2 years ago
  5. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Are you saying n is an eigenvector ?

    • 2 years ago
  6. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    honesly i dont know wat to do. this is what the teacher asked us

    • 2 years ago
  7. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Or are you say An is the matrix?

    • 2 years ago
  8. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    idk..lol

    • 2 years ago
  9. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok I think |dw:1340595284758:dw| and |dw:1340595304816:dw|

    • 2 years ago
  10. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Is that what you think?

    • 2 years ago
  11. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    But that doesn't make since that A_n would be the matrix with nothing but zero entries

    • 2 years ago
  12. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    do you mean the determinant is 0?

    • 2 years ago
  13. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |A_n|=0?

    • 2 years ago
  14. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    that would make since

    • 2 years ago
  15. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sense*

    • 2 years ago
  16. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I think that is what you mean

    • 2 years ago
  17. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so do you know how to find the determinant of a matrix?

    • 2 years ago
  18. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ya ad-bc

    • 2 years ago
  19. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Try finding the determinant of A_2 ? What do you get?

    • 2 years ago
  20. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    zero

    • 2 years ago
  21. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok what about A_3

    • 2 years ago
  22. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    same

    • 2 years ago
  23. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok so we have convinced ourselves that |A_n|=0 But we must prove it

    • 2 years ago
  24. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1340595692432:dw|

    • 2 years ago
  25. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I would just show a little work for this show a pattern you know

    • 2 years ago
  26. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    like how you did for A_3 and then do the nth term you know what I mean?

    • 2 years ago
  27. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    how do u find determinant for 3x3 or bigger matrix?

    • 2 years ago
  28. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok for an A_3 |dw:1340595913293:dw|

    • 2 years ago
  29. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1340595950507:dw|

    • 2 years ago
  30. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The signs alternate

    • 2 years ago
  31. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Like you take top entries

    • 2 years ago
  32. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    only the first row?

    • 2 years ago
  33. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    And take everything that isn't below that entry

    • 2 years ago
  34. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    like if its 10x10 u still only do the first row /?

    • 2 years ago
  35. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    For |A_4| |dw:1340596049002:dw|

    • 2 years ago
  36. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1340596102188:dw|

    • 2 years ago
  37. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and you already know how to find the determinant for a 3 by 3

    • 2 years ago
  38. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Same thing just take the top entries and do the signs alternating

    • 2 years ago
  39. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ A=\left( \begin{array}{cccc} 0 & 1 & 2 & 3 \\ 0 & 0 & 1 & 4 \\ 0 & 0 & 0 & 3 \\ 0 & 0 & 0 & 0 \\ \end{array} \right)\\ A^2=\left( \begin{array}{cccc} 0 & 0 & 1 & 10 \\ 0 & 0 & 0 & 3 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \end{array} \right)\\ A^3=\left( \begin{array}{cccc} 0 & 0 & 0 & 3 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \end{array} \right)\\ A^4=\left( \begin{array}{cccc} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \end{array} \right) \]

    • 2 years ago
  40. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but the determinant of the new 3x3 is gonna also be broken down right? .. im ur case its zero bec the coefficient is zero so it odsnt really mater

    • 2 years ago
  41. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes just like i did above for the 3 by 3

    • 2 years ago
  42. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    But not all the top entries are 0

    • 2 years ago
  43. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @eliassaab i dont really understnad wat u wrote

    • 2 years ago
  44. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    right...

    • 2 years ago
  45. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    See my example below and examine what is going on?

    • 2 years ago
  46. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    you have zeros. but what are you doing to the matrix?

    • 2 years ago
  47. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you think he means to raise A to a power @eliassaab ?

    • 2 years ago
  48. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Instead of finding the determinant ?

    • 2 years ago
  49. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You raise it to the power 2, then 3, then 4.

    • 2 years ago
  50. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok I'm sorry @liliy I don't know what your question is asking anymore.

    • 2 years ago
  51. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You do not need to deal with determina

    • 2 years ago
  52. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    determinant

    • 2 years ago
  53. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so can you start over with me?

    • 2 years ago
  54. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    what does a^n=0 even mean?

    • 2 years ago
  55. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Any matrix like yours, when you raise it to the power 2, you get what is first above the diagonal is zero When you raise it to the power 2, you get the first and the second above the diagonal to be zero. When you raise it to the power 3, you get the first and the second and third above the diagonal to be zero. When you raise it to the power 4, you get everything zero.

    • 2 years ago
  56. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Look at A^4 in my example above to see that A^4=0, this means all the entries of the matrix A^4 are zeros.

    • 2 years ago
  57. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So you are just giving another way right @eliassaab Do you think I interpreted is question correctly?

    • 2 years ago
  58. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @myininaya, you do not need determinant to do that,

    • 2 years ago
  59. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah I know, but I'm asking you if I interpreted it correctly?

    • 2 years ago
  60. liliy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @eliassaab i dont undesrtnad how you started to do the problem. my teacher said start with a^2 .. and move to bigger ones... so wat is a= to a 4x4 and then writing a^2... a^3..

    • 2 years ago
  61. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Here is a quick proof using the characteristic polynomial f(x) of the matrix A that says the f(A)=0. Our matrix has\( f(x)=x^n\), hence \(f(A)=A^n=0\)

    • 2 years ago
    • Attachments:

See more questions >>>

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.