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Matrix Algebra to decode a message

  1. May 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Hey, I need to decode a message hidden in a Matrix as a practice activity, and I'm rather stuck.

    The alphabet key is starting from the letter A,numbered using first:
    a)Fibonacci Sequence
    b)Prime Numbers
    c)Counting Numbers
    d)No numbers higher than 27

    http://latex.sidoh.org/?render64=WD1cWyBcbGVmdCggXGJlZ2lue2FycmF5fXtjY2N9DQoxICYgMCAmIDEgXFwNCjAgJiAxICYgMCBcXA0KMSAmIDAgJiAxIFxlbmR7YXJyYXl9IFxyaWdodClcXQ== [Broken]
    http://latex.sidoh.org/?render64=WT1cWyBcbGVmdCggXGJlZ2lue2FycmF5fXtjY2N9DQotMiAmIDIgJiAxIFxcDQowICYgMiAmIDQgXFwNCi0yICYgNCAmIDQgXGVuZHthcnJheX0gXHJpZ2h0KVxd [Broken]
    http://latex.sidoh.org/?render64=VT1cWyBcbGVmdCggXGJlZ2lue2FycmF5fXtjY2N9DQo0MiAmIDEyMSAmIDEzMSBcXA0KMjUgJiA5MyAmIDkyIFxcDQoyNyAmIDk3ICYgOTcgXFwNCjI5ICYgMTExICYgMTEyIFxcDQo3ICYgMzYgJiAzMiBcXA0KMzQgJiA4OCAmIDk4IFxlbmR7YXJyYXl9IFxyaWdodClcXQ== [Broken]
    Now we have the hard part, we have to use "matrix algebra" (which we learnt over a month ago) to find the real message. An instinct tells me I have to either find an inverse or identity, but I don't know how to do that with a matrix.


    2. Relevant equations
    The encoded matrix, U, is the product of (X+Y)^T


    3. The attempt at a solution
    Not a whole heap since I only have a sheet and now textbooks, but still I did the alphabet key:
    Code (Text):

    First we have to solve the alphabet key, which I've done:
    A=1
    B=2
    C=3
    D=5
    E=8
    F=13
    G=21
    H=7
    I=11
    J=17
    K=19
    L=23
    M=4
    N=6
    O=9
    P=10
    Q=12
    R=14
    S=15
    T=16
    U=18
    V=20
    W=22
    X=24
    Y=25
    Z=26
    Space=27
    And I know I have to times something by an inverse or identity, but I don't know what. THe only thing I can remember on Matrix algebra is AX=something.








    I know this is not the greatest attempt, but I've worked 17 hours this weekend, I have no idea what to do, and after this I still have to work out how to reencode a message (which I should hopefully be able to work out)
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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