We perform the Gauss-Jordan elimination
((2,5,-2,14),(5,-6,2,0),(4,-1,3,-7))
Exchange R2 harr R1
((5,-6,2,0),(2,5,-2,14),(4,-1,3,-7))
Divide R1 by 5
((1,-1.2,0.4,0),(2,5,-2,14),(4,-1,3,-7))
R2 harr R2-2R1
((1,-1.2,0.4,0),(0,7.4,-2.8,14),(4,-1,3,-7))
R3 harr R3-4R1
((1,-1.2,0.4,0),(0,7.4,-2.8,14),(0,3.8,1.4,-7))
R2 harr (R2)/7.4
((1,-1.2,0.4,0),(0,1,-0.378,1.892),(0,3.8,1.4,-7))
R3 harr R3-3.8R2
((1,-1.2,0.4,0),(0,1,-0.378,1.892),(0,0,2.838,-14.189))
R3 harr (R3)/2.838
((1,-1.2,0.4,0),(0,1,-0.378,1.892),(0,0,1,-5))
R1 harr R1-0.4R3
((1,-1.2,0,2),(0,1,-0.378,1.892),(0,0,1,-5))
R2 harr R2+0.378R3
((1,-1.2,0,2),(0,1,0,0),(0,0,1,-5))
R1 harr R1+1.2R2
((1,0,0,2),(0,1,0,0),(0,0,1,-5))