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Indcidence Matrices

  1. May 29, 2013 #1
    Should the right answer to this question(below) be 14 and not 31? because
    A[itex]_{ij}[/itex][itex]^{k}[/itex] means number of paths from i to j of length K. So A[itex]_{12}[/itex][itex]^{8}[/itex] = 14

    We then represent the graph as indcidence matrices and go from there on:

    A = { {0,1,0,0}, {1,0,1,0}, {1,1,0,1}, {1,0,0,0} }

    A[itex]^{8} = { {22,14,13,4}, {31,35,14,13}, {40,31,22,10}, {10,13,4,5} }

    QUESTION:
    At each step the elevator is able to travel directly from floor to floor as listed below. Suppose we go floor to floor eight times (e.g 1 to 2 then 2 to 3 would be two times). How many different ways can we start at floor 1 and end at floor 2?

    floor 1 to floor 2
    floor 2 to floor 3
    floor 3 to floor 4
    floor 4 to floor 1
    floor 2 to floor 1
    floor 3 to floor 1
    floor 3 to floor 2


    Correct Answer in the back of the book: 31
     
    Last edited: May 29, 2013
  2. jcsd
  3. May 29, 2013 #2

    Ray Vickson

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    I would not call the book's answer "correct"; I get exactly the same ##A^8## answer as you.
     
    Last edited by a moderator: May 6, 2017
  4. May 29, 2013 #3
    I guess they mixed it up then, I guess 31 is the answer from floor 2 to floor 1 then. Thanks for the reply.
     
  5. May 29, 2013 #4

    haruspex

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    I agree. Quibble: the matrix is the adjacency matrix, not the incidence matrix, right?
     
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