Reduced Row Echelon/Solution Set Problem

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The discussion revolves around understanding the solution set of two linear systems using reduced row echelon forms. It clarifies that a matrix can yield zero, one, or infinitely many solutions, depending on the relationship between the number of equations and unknowns. The provided matrix indicates an infinite number of solutions due to having more unknowns than equations. Participants suggest introducing parameters to express the variables in terms of these parameters for clarity. The conversation emphasizes that once in reduced row echelon form, the solution set becomes more apparent.
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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.
 
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After solving a matrix you will have either zero, one, or an infinite number of solutions. For example the solution x_{1}=0 x_2=0 x_3=0 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.
 
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.
 
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 x_4=5+x_5 and x_3=15+5x_5 and x_1=11+3x_5-2x_2.

If you set x_5=t and x_2=s you should be able to solve for each variable in terms of s and t.
 
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That was very helpful.
Thanks a million.
 
welcome :DD
 
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