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Matrices: word problem, transition matrix

  1. Sep 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Hello!
    Please, take a look at the problem described in the attached file.
    The question is: Explain why the transition matrix does what we want it to do.


    2. Relevant equations



    3. The attempt at a solution
    (sorry, I don't know yet how to type formulas)
    I don't quite understand this transition matrix.
    0.90 0.20
    0.10 0.80

    I assume that the first column refers to Tribune readers and second one to Picayune readers.
    Then the fist row should refer to those who are loyal to T and P, respectively; and second row - to those who would like to switch.
    But textbook option suggests a different view.
    Please, help me to understand this matrix.

    Thank you!
     

    Attached Files:

  2. jcsd
  3. Sep 23, 2014 #2
  4. Sep 23, 2014 #3
    Thank you for reply. I don't understand how and why this matrix was formed in the first place (as I have stated in my questions); that is why given data is reflected in this particular manner.
    As to multiplication, if I have understood that correctly, we can't multiply 2x2 matrix (which is Q in this case) by 1x1 matrix (X).
    I would be grateful for the help.
    Thank you!
     
  5. Sep 23, 2014 #4
    X is not a 1x1 matrix, it's 2x1. X is
    [tex]
    \begin{pmatrix}
    T\\
    P
    \end{pmatrix}
    [/tex]
    That is, the top number is T, the number of people who get the Tribune, and the bottom number Q is the number that get the Picayune.So you can multiply Q and X, because Q is 2x2.

    It looks like you need to revise matrix multiplication. How would you multiply
    [tex]
    \begin{pmatrix}
    1 & 2\\
    3 & 4
    \end{pmatrix}
    [/tex]
    with
    [tex]
    \begin{pmatrix}
    5\\
    6
    \end{pmatrix}
    [/tex]
    If you can do that, then you can multiply Q and X, it's just that X has letters instead of numbers
     
  6. Sep 27, 2014 #5
    Yes, thank you. I've figured this out. Thank you for the help!
    Just to show that I understand it now:

    (17 39)
     
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