What kind of form is this general solution of a system?

[brownman]

If this were the reduced row echelon form of an augmented matrix,

1 2 0 1 1 0 3
0 0 1 2 1 0 1
0 0 0 0 0 1 2
0 0 0 0 0 0 0

What is the form of the following answer given, and how can I understand it?

(x1; x2; x3; x4; x5; x6) = (3; 0; 1; 0; 0; 2)+ t(1; 0; 1; 0; 1; 0)+ s(1; 0; 2; 1; 0; 0)+ u(2; 1; 0; 0; 0; 0)
for s; t; u $\in$ ℝ.

 

[halo31]

the solution to the system is written in parametric form where T,S,U are your free variables and (3 0 1 0 0 2) is your particular solution.