Matrix format:
( 1 2 3 | 1 )
( 2 3 4 | 3 )
( 1 2 1 | 3 )
R3-R1:
( 1 2 3 | 1 )
( 2 3 4 | 3 )
( 0 0 -2 | 2 )
R3/-2:
( 1 2 3 | 1 )
( 2 3 4 | 3 )
( 0 0 1 | -1 )
R2-R1:
( 1 2 3 | 1 )
( 1 1 1 | 2 )
( 0 0 1 | -1 )
R1⇔R2:
( 1 1 1 | 2 )
( 1 2 3 | 1 )
( 0 0 1 | -1 )
R2-R1:
( 1 1 1 | 2 )
( 0 1 2 | -1 )
( 0 0 1 | -1 )
R2-R3:
( 1 1 1 | 2 )
( 0 1 1 | 0 )
( 0 0 1 | -1 )
R1-R2:
( 1 0 0 | 2 )
( 0 1 1 | 0 )
( 0 0 1 | -1 )
R2-R3:
( 1 0 0 | 2 )
( 0 1 0 | 1 )
( 0 0 1 | -1 )
x1=2; x2=1; x3=-1.