Is this a ladder matrix? 1 2 3 4 0 2 3 4 0 4 5 6 0 6 7

Is this a ladder matrix? 1 2 3 4 0 2 3 4 0 4 5 6 0 6 7

1 2 3 4
0 2 3 4
0 4 5 6
0 0 6 7
It's not. The first nonzero element is a11, A22, A32, A43
The row mark is increased, but the column mark is 1,2,2,3, which is not strictly increased

Finding simplified ladder matrix 13 - 7 - 8 25 4 4 - 3 - 7 - 2 - 3 14 - 12 - 15
1 3 -7 -8
2 5 4 4
-3 -7 -2 -3
1 4 -12 -15

r3+r1+r2,r2-2r1,r4-r11 3 -7 -80 -1 18 200 1 -5 -70 1 -5 -7r1-3r3,r2+r3,r4-r31 0 8 130 0 13 130 1 -5 -70 0 0 0r2*(1/13),r1-8r2,r3+5r21 0 0 50 0 1 10 1 0 -20 0 0 0-->1 0 0 50 1 0 -20 0 1 10 0 0 0

How to transform 2 34 5 6 1 2 000 to row ladder matrix?

2 3 4 5 6
1 1 1 1 1
1 2 0 0 0
r1-2r2,r3-r2
0 1 2 3 4
1 1 1 1 1
0 1 -1 -1 -1
r3-r1
0 1 2 3 4
1 1 1 1 1
0 0 -3 -4 -5
r1r2
1 1 1 1 1
0 1 2 3 4
0 0 -3 -4 -5
--This is a row ladder matrix