I have the following system of linear equations.
$\ 4x+y+z+t=6$
$\ -x-3y+z+w=6$
$\ 2x+y+5z-w-t=6$
$\ -x-y-z+4w=6$
$\ 2x-z+w+4t=6$
We are supposed to find the variants of the above system for which the Gauss-Seidel method converges. I tried performing row operations to it, but it yielded no results, to the best of my ability. The matrix, with w and t, for me comes to be:
[4 1 1 1 0 1]
[-1 -3 1 1 0]
[2 1 5 -1 -1]
[-1 -1 -1 4 0]
[2 0 -1 1 4]
Can anyone point out what I am doing wrong and what one particular variant of this system could be?
Edit: I do know that the system in its original form does yield convergence, but the task is to find other forms as well.