1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrix Algebra

  1. Dec 18, 2008 #1
    In a certain country, there are three political parties: The conservative Butter-side-up party
    (the Uppers), the radical Butter-side-down party (the Downers), and the progressive Pitapocket
    party (the Pocketeers). Recent polls show that each year, 70% of Uppers remain
    Uppers, 80% of Downers remain Downers, 40% of Pocketeers remain Pocketeers. Everyone
    else switches, and they divide equally among the other two parties.
    (a) Write the transition matrix representing the party-switching process.
    (b) In the long run, how will the people be distributed among the political parties?
     
  2. jcsd
  3. Dec 18, 2008 #2

    Vid

    User Avatar

    What have you tried?
     
  4. Dec 18, 2008 #3
    .7 .15 .15
    .8 .2 .2
    .4 .3 .3


    is that say matrix A?
     
  5. Dec 18, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, that's not correct. Assuming (A, B, C) means that one year A% uppers, B% downers, C% pitas, then you must have
    [tex]\left[\begin{array}{ccc}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a{_33}\end{array}\right]\left[\begin{array}{c}1.0 \\ 0.0 \\ 0.0\end{array}\right]= \left[\begin{array}{c} 0.7 \\ 0.15 \\ 0.15\end{array}\right][/tex]

    [tex]\left[\begin{array}{ccc}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]\left[\begin{array}{c}0.0 \\ 1.0 \\ 0.0\end{array}\right]= \left[\begin{array}{c} 0.1 \\ 0.8 \\ 0.1\end{array}\right][/tex]
    and
    [tex]\left[\begin{array}{ccc}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]\left[\begin{array}{c}0.0 \\ 0.0 \\ 1.0\end{array}\right]= \left[\begin{array}{c} 0.3 \\ 0.3 \\ 0.4\end{array}\right][/tex]

    You can determine the "a"s from that.
     
  6. Dec 18, 2008 #5
    .7 .1 .3
    .15 .8 .3
    .15 .1 .4





    then do i just reduce the matrix equation and find the values?
     
  7. Dec 18, 2008 #6
    or do i find the eigenvalues and eigenvectors?
     
  8. Dec 19, 2008 #7

    Mark44

    Staff: Mentor

    Have you tried what Halls suggested?
     
  9. Dec 19, 2008 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    C'mon now, you are not coming to this having no idea what you are doing are you? WHY would you "reduce the matrix equation" (what matrix equation) or "find the eigenvalues and eigenvectors"? What would either of those tell you?

    Intrepret "in the long run as meaning "after many years". After n years, You will have An X where X is the initial distribution. How can you most easily find An for large n?

    He did- in post #5.
     
  10. Dec 19, 2008 #9
    I took .7 , .8 , and .4 and subtracted 1 from each, then i got x1=6t x2=3t and x3=t
    so 60% uppers, 30% downers 10% pocketeers, is that close or am i just way off
     
  11. Dec 20, 2008 #10

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What reasoning did you use to arrive at that answer?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Matrix Algebra
  1. Matrix Algebra (Replies: 2)

  2. Matrix ALgebra (Replies: 2)

  3. Matrix algebra (Replies: 1)

  4. Matrix Algebra (Replies: 1)

Loading...