I have the following system of equations:
x1 + 6x2 + 2x3 - 5x4 = 0 -x1 - 6x2 - x3 - 3x4 = 0 2x1 + 612x2 + 5x3 - 18x4 = 0
and I understand that it translated into the following matrix:
1 6 2 -5 0 -1 -6 -1 -3 0 2 12 5 -18 0
Finally, I understand how to use Gauss-Jordan elimination to change this to reduced row-echelon form:
1 6 0 11 0 0 0 1 -8 0 0 0 0 0 0
However, in an example solution that my instructor has prepared, this is then used to find the general solution in parametric form:
x1 = -6s - 11t x2 = s x3 = 8t x4 = t
No intermediate steps are given. I can see that a similarity in the numbers, but I'm not sure exactly what to do.
It looks like arbitrary letter variables have been assigned to those columns which don't start any row with a one and then these variables are used to complete equations for the columns which do start rows. Is that all this is? Or is there something that I'm missing?