Solving a system in terms of intersecting planes

  1. 1. The problem statement, all variables and given/known data

    x + 4y + z = 0
    4x + 13y + 7z = 0
    7x + 22y + 13z = 1


    2. Relevant equations



    3. The attempt at a solution

    x + 4y + z = 0
    - 3y + 3z = 0
    -6y + 6z = 1

    x + 4y + z = 0
    -y + z = 0
    -6y + 6z = 1

    Then whichever way I solve it I have 0=1 or 0=1/6, so where to go from here or is there just no solution?
     
    Last edited: Feb 5, 2007
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,302
    Staff Emeritus
    Science Advisor

    First of all, the problem statement is NOT just
    x + 4y + z = 0
    4x + 13y + 7z = 0
    7x + 22y + 13z = 1

    That's not a "problem", that's a system of equations. What are asked to do with them?
     
  4. Sorry I had only put it in the title of the thread.

    Find all solutions of the linear system. Describe your solution in terms of intersecting planes.
     
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