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Lenear system question

  1. Dec 11, 2009 #1
    why lenear system has a single solution?
     
  2. jcsd
  3. Dec 11, 2009 #2

    Mark44

    Staff: Mentor

    In general, a linear system of equations can have no solution, a single solution, or an infinite number of solutions. Do you have a question about a particular linear system?
     
  4. Dec 11, 2009 #3
    it for electrical circuit theory

    for thevenin theorem

    i have a pi system which has independent sources

    and my prof said

    "we have a lenear system so the is a single solution"

    i cant understand why?
     
  5. Dec 11, 2009 #4

    Mark44

    Staff: Mentor

    I don't know what a "pi system" is. In any case, unless you know something about the linear system, you can't tell how many solutions it has.

    Here are three very simple examples:

    1. No solutions
    x + 2y = 3
    x + 2y = 4

    2. Exactly one solution
    x + y = 3
    x - y = 1
    (solution is x = 2, y = 1)

    3. Infinite number of solutions
    x + y = 3
    2x + 2y = 6
     
  6. Dec 12, 2009 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Note Mark44's options: one solution, no solution, infinite number of solutions.

    If you know the problem has a non-zero finite number of solutions then you can say there is a single solution- as opposed to, say, a quadratic equation in which there can be two solutions.
     
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