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How do you solve equations with matrices?

  1. Apr 9, 2012 #1
    How do you solve equations that have matrices?
    heres an example (its just off the top of my head)

    3x+y=z+4 where
    x=1 0 0 0
    0 1 0 0
    0 0 1 0
    0 0 0 1
    and y=0 0 0 1
    0 0 1 0
    0 1 0 0
    1 0 0 0
    and a follow up question; does the process change if coordinates are involved in the equation?
    if so, how?
     
  2. jcsd
  3. Apr 9, 2012 #2

    AlephZero

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    Your equation doesn't make any sense. On the left hand side, if x and y are 1x4 matrices then 3x+y is a 1x4 matrix. That's OK. The left hand side is the matrix 3 0 0 4.

    So the right hand side must also be a 1x4 matrix, but can't add a matrix to the scalar "4".

    I have no idea what you think the array of numbers after the equation means.
     
  4. Apr 10, 2012 #3
    I will answer your question assuming that you meant 4 to be 4*E, where E is the identity matrix of GL(4,R) (i.e x=E).

    To solve the system you are given you simply reduce it to a simple equation in each entry. So if we denote by Xij, Yij, Zij, Eij the entry in the ith row, jth column of X,Y,Z,E respectively, the equation becomes:

    3Xij+Yij=Zij+4Eij

    for every i and every j. Rearrange:

    Zij=3Xij+Yij-4Eij

    Hence Z is the matrix:

    -1 0 0 1
    0 -1 1 0
    0 1 -1 0
    1 0 0 -1

    Hope that helps :smile:
     
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