Question 958270
The beginning matrix is

1  1  1  2
2 -3  1 -11
-1 2 -1  8

add 1 times the 1st row to the 3rd row
1  1  1  2
2 -3  1 -11
0  3  0  10

add -2 times the 1st row to the 2nd row
1  1  1  2
2 -5 -1 -15
0  3  0  10

add 3/5 times the 2nd row to the 3rd row
1  1    1   2
0 -5   -1  -15
0  0  -3/5  1

multiply the 3rd row by -5/3
1  1    1   2
0 -5   -1  -15
0  0    1  -5/3

add -1 times the 3rd row to the 1st row
1  1    0   11/3
0 -5   -1  -15
0  0    1  -5/3

add -1 times the 3rd row to the 2nd row
1  1    0   11/3
0 -5   0   -50/3
0  0    1  -5/3

multiply the 2nd row by -1/5
1  1    0   11/3
0 -5   0   -50/3
0  0    1  -5/3

add 1 times the 3rd row to the 2nd row
1  1    0   11/3
0  1    0   10/3
0  0    1  -5/3

add -1 times the 2nd row to the 1st row
1  0    0   1/3
0  1    0   10/3
0  0    1  -5/3