Here is the complete succession of row operations.

1

2
2

3
1

6
 6 R1
2
1

4
1

2
4 R2
3
4
1
8
1
2
3 R2 + 8 R1
3
4
1
0
35
14
1

7
 R2
3
4
1
 5 R14 R2
0
5
2
15
0
3
1

15
 R1
0
5
2
1

5
 R2
1
0
1

5
0
1
2

5