The first row is 1,2,3,4, the second row is 0,1,2,3, the third row is 0,0,1,2, the fourth row is 0,0,0,1. By using the elementary row transformation method, the inverse matrix of the invertible matrix is obtained,

The first row is 1,2,3,4, the second row is 0,1,2,3, the third row is 0,0,1,2, the fourth row is 0,0,0,1. By using the elementary row transformation method, the inverse matrix of the invertible matrix is obtained,

Hello, I have sent you the picture

How can a = 1 - 12 10 2 - 24 20 3 06 - 1 10 3 00 1 be reduced to the simplest row ladder matrix?
A= ( 1 -1 2 1 0) (2 -2 4 2 0 ) (3 0 6 -1 1) (0 3 0 0 1)

r2-2r1,r3-3r1
1 -1 2 1 0
0 0 0 0 0
0 3 0 -4 1
0 3 0 0 1
r4-r3
1 -1 2 1 0
0 0 0 0 0
0 3 0 -4 1
0 0 0 4 0
Exchange will do
1 -1 2 1 0
0 3 0 -4 1
0 0 0 4 0
0 0 0 0 0
-->
1 0 2 0 1/3
0 1 0 0 1/3
0 0 0 1 0
0 0 0 0 0

How to transform (2, - 1, - 1,1,2; 1,1, - 2,1,4; 4, - 6,2, - 2,4; 3,6, - 9,7,9) into row ladder matrix

r3-2r1,r1-2r2,r4-3r2
0 -3 3 -1 -6
1 1 -2 1 4
0 -4 4 -4 0
0 3 -3 4 -3
r3*(-1/4),r1+3r3,r4-3r3
0 0 0 2 -6
1 1 -2 1 4
0 1 -1 1 0
0 0 0 1 -3
r1-2r4
0 0 0 0 0
1 1 -2 1 4
0 1 -1 1 0
0 0 0 1 -3
Exchange bank
1 1 -2 1 4
0 1 -1 1 0
0 0 0 1 -3
0 0 0 0 0