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Simplying a matrix equation

  1. Nov 12, 2007 #1
    x+2y y+2t = 5x -y

    4x+3z 4y+3t = 5z -t

    Iam just not sure how they simplified these equations to this:

    z = 2x, t = -y??

    Please help.
  2. jcsd
  3. Nov 12, 2007 #2


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    Your notation is confusing. You have a blank in the first equation between 2y and y. Similarly in the second equation between 3z and 4y. What do you mean??
  4. Nov 12, 2007 #3
    The two are separate matrices

    Like one is
    x+2y y+2t
    4x+3z 4y+3t

    And the other is
    5x -y
    5z -t

    And they set them equal and simplify to

    z = 2x, t = -y

    I dont get how they got that?
  5. Nov 12, 2007 #4


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    You have a 4x4 matrix on the left.

    What is on the right?
  6. Nov 12, 2007 #5
    I have no 4x4

    one matrix is 2x2:

    (First column)
    (Second Column)

    Second matrix is 2x2:

    (First column)
    (Second Column)
    Last edited: Nov 12, 2007
  7. Nov 13, 2007 #6


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    Now that we have it clear that these are matrices, they must give, since two matrices are equal if and only if their corresponding entries are equal,
    x+2y= 5x, y+ 2t= -y, 4x+ 3z= 5z, and 4y+ 3t= -t.
    The third equation is just 4x= 2z (subtract 3z from both sides). Also, the fourth equation is the same as 4y= -4t (subtract 3t from both sides) so t= -y as claimed.
  8. Nov 13, 2007 #7
    Ahh I understand now... Thank you so much for the help.
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