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The form of a Matrix M help.

  1. Apr 19, 2004 #1
    I need help finding the form of the matrix M, heres the question:
    (n and n+1 is a subscript):

    Xn =
    [An]
    [Bn]

    Xn+1 = MXn

    M is a 2 x 2 matrix. The question says - What is the precise form of the matrix M?
     
  2. jcsd
  3. Apr 19, 2004 #2

    HallsofIvy

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    Science Advisor

    You are going to need more information than that! For one thing, are An and Bn numbers? The real information you need is some definition of xn. Just "xn+1= Mxn isn't enough. Do you have formulas for An and Bn?
     
  4. Apr 19, 2004 #3
    o sorry, the other information given is that the vectors with two components are A, & B so yes they are numbers. (which represents the concentration of a reactant-for the question).
    After one time step (where n represents the timesteps thus n+1) 80% of A is transformed into B while 60% of B is tranformed into A.

    Does this help?
     
  5. Apr 23, 2004 #4

    HallsofIvy

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    Science Advisor

    So An+1= 0.2An+ 0.6Bn (the 20% of A left over after 80% is transformed into B and the 60% of B that is transformed into A) and
    Bn+1= 0.8An+ 0.4Bn.

    Looks like M=
    [0.2 0.6]
    [0.8 0.4]
     
    Last edited by a moderator: Apr 23, 2004
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