Results 1 to 5 of 5

Math Help - Matrix division/inverse problem

  1. #1
    Newbie
    Joined
    Apr 2010
    From
    Iowa
    Posts
    20

    Matrix division/inverse problem

    Edmonton’s mayor is getting nervous about the upcoming municipal elections and wants to send a private message to his counsellors. One of his interns is taking linear algebra and helps him set up a matrix 𝑀 where each letter in the message is replaced by the number of its position in the alphabet. Thus, for example, “ESPIONAGE” becomes the matrix M=[5 19 16, 9 15 14, 1 7 5] (its a 3 x 3 matrix each comma representing a different row.

    In order to avoid detection each message sent to counsellors is encoded as MK,
    where K=[1 -3 0, -2 5 1, 0 1 0] ( 3x3 matrix as well) If the counsellors receive the matrix x [-8 29 15, -7 30 6, -8 16 13] what is the mayor trying to tell them?

    so I did this:
    MK=X
    M(k^-1)k=(k^-1)x
    M=(k^-1)x

    Found the inverse of K so thats K^-1 and times it towards matrix X. I get negative numbers in the final matrix and numbers above 26 so i can't figure out the "code."

    The K inverse is [1 0 3, 0 0 1, 2 1 1] what did I do wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,591
    Thanks
    1445
    That's because if your equation is

    MK = X

    then

    MKK^{-1} = XK^{-1}

    MI = XK^{-1}

    M = XK^{-1}.

    You should have postmultiplied by the inverse of K.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2010
    From
    Iowa
    Posts
    20
    Could you explain what you meant by "Postmultiplied by the inverse of K"?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,591
    Thanks
    1445
    XA is premultiplying by X because the X goes in front.

    AX is postmultiplying by X because the X goes behind.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2010
    From
    Iowa
    Posts
    20
    Wow....Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Derivative of a matrix inverse and matrix determinant
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 24th 2011, 08:18 AM
  2. Matrix Inverse Problem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 10th 2010, 01:39 PM
  3. Inverse matrix problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 17th 2010, 01:20 AM
  4. Inverse matrix problem
    Posted in the Algebra Forum
    Replies: 0
    Last Post: May 16th 2010, 09:59 PM
  5. Inverse matrix problem
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 4th 2010, 02:02 PM

Search Tags


/mathhelpforum @mathhelpforum