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Reduced Row Echelon/Solution Set Problem

  1. Oct 18, 2009 #1
    The question reads "Use the reduced row echelon forms that you computed to describe the solution set for each of two linear systems we consider".

    What I don't understand is what it means by The solution set for each of the two linear systems.
    Could someone clear this up for me.

    Any help appreciated.
    Thanks.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 18, 2009 #2
    After solving a matrix you will have either zero, one, or an infinite number of solutions. For example the solution [tex]x_{1}=0[/tex] [tex] x_2=0[/tex] [tex] x_3=0[/tex] might be the solution set to a homogeneous system. Once you get the matrix to reduced row form the solution set should be apparent just from looking at the matrix.
     
  4. Oct 18, 2009 #3
    OK, I'm not really sure what the answer is.
    One of my matrices is
    1 2 0 0 -3 11
    0 0 1 0 -5 15
    0 0 0 1 -1 5

    Could you point me in the right direction please.
     
  5. Oct 18, 2009 #4
    Well that particular matrix will have an infinite number of solutions because you have more unknowns than equations. The matrix is already reduced as much as possible I believe. In this situation you would generally introduce one or more parameters and back substitute.

    For example according to your matrix [tex]x_4=5+x_5[/tex] and [tex]x_3=15+5x_5[/tex] and [tex]x_1=11+3x_5-2x_2[/tex].

    If you set [tex]x_5=t[/tex] and [tex]x_2=s[/tex] you should be able to solve for each variable in terms of s and t.
     
    Last edited: Oct 18, 2009
  6. Oct 18, 2009 #5
    That was very helpful.
    Thanks a million.
     
  7. Oct 18, 2009 #6
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