Reduced Row Echelon/Solution Set Problem

[iasc]

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.

 

[206PiruBlood]

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.

 

[iasc]

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.

 

[206PiruBlood]

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.

 

[iasc]

That was very helpful.
Thanks a million.

 

[206PiruBlood]

welcome