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All zero row in linear algebra

  1. Jan 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Say you had an augmented matrix

    0 1 0 0
    0 0 1 0
    0 0 0 0

    You would get...

    x2=0
    x3=0
    x1= arbitrary?

    What exactly is meant by arbitrary?
    Does this mean that x1 could be anything?

    and if so does that mean that the system has an infinite amount of solutions because x1 can be an infinite amound of numbers?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 17, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    There are no equations x1 has to satisfy. Yes, x1 equals anything. And sure, that means you have an infinite number of (x1,x2,x3) values that work.
     
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