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I Solving a system of equation with matrices

  1. Feb 7, 2017 #1
    I have the following system of equations: ##2t-4s=-2;~-t+2s=-1;~3t-5s=3##. With them, I form the matrix
    \begin{bmatrix}
    2 & -4 & -2 \\
    -1 & 2 & -1 \\
    3 & -5 & 3
    \end{bmatrix}
    Which turns out to be row equivalent to
    \begin{bmatrix}
    1 & 0 & 11 \\
    0 & 1 & 6 \\
    0 & 0 & 0
    \end{bmatrix}
    so ##s=11,~t=6##. However, this satisfies only the first and third equation and not the second. Shouldn't it satisfy all of the equations, since I got a valid result from doing row reduction?
     
    Last edited: Feb 7, 2017
  2. jcsd
  3. Feb 7, 2017 #2

    fresh_42

    Staff: Mentor

    Have you worked with ##A_{23}=-1## as in your second equation, or with ##A_{23}=-2## in your matrix?
    And can the first two equations hold true simultaneously at all?
     
  4. Feb 7, 2017 #3
    I fixed it. Am I doing the row reduction wrong? Should I be getting an inconsistent system?
     
  5. Feb 7, 2017 #4

    fresh_42

    Staff: Mentor

    Multiply the second equation by ##-2## and compare it with the first.
     
  6. Feb 7, 2017 #5
    2t - 4s = -2 and 2t - 4s = 2, which cannot be possible. So I guess I just did the row reduction wrong.
     
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