Results 1 to 3 of 3

Math Help - Discrete math matrix?

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    71

    Discrete math matrix?

    How do I show:

    Given we let A=:
    |1 1|
    |1 0|
    That:
    A^n is equal to the matrix:
    |fn+1 fn|
    |fn fn-1|

    for whenever R is positive.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by orendacl View Post
    How do I show:

    Given we let A=:
    |1 1|
    |1 0|
    That:
    A^n is equal to the matrix:
    |fn+1 fn|
    |fn fn-1|

    for whenever R is positive.
    Hi

    Let A^n = \left(\begin{array}{cc}a_n&b_n\\c_n&d_n\end{array}  \right)

    Then A^{n+1} = A \cdot A^n = \left(\begin{array}{cc}a_n+c_n&b_n+d_n\\a_n&b_n\en  d{array}\right)

    Therefore
    a_{n+1} = a_n + c_n
    b_{n+1} = b_n + d_n
    c_{n+1} = a_n
    d_{n+1} = b_n

    The first and third relations give a_{n+2} = a_{n+1} + c_{n+1} = a_{n+1} + a_n

    The second and fourth relations give b_{n+2} = b_{n+1} + d_{n+1} = b_{n+1} + b_n

    Check the first terms of a_n and b_n to determine the index of f

    The third and fourth relations give the rest of the solution
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    71

    ??? Here is what I have so far:

    I said that the relation for 3rd and 4th should be:
    cn+2 = cn+1+dn+1 = cn+1+bn

    I tried everything except I do not know what to do given the relations for the problem...

    Any follow up suggestions?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Discrete math
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 7th 2009, 10:30 PM
  2. Discrete Math - HELP
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 8th 2008, 02:22 PM
  3. New to discrete math
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 30th 2008, 03:55 AM
  4. please help with discrete math
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 13th 2008, 01:57 PM
  5. Discrete Math
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: April 26th 2007, 05:30 PM

Search Tags


/mathhelpforum @mathhelpforum