线性代数 矩阵化为标准型阶梯矩阵

1 -1 2 1 0
2 -2 4 2 0
3 0 6 -1 1
3 0 6 3 1
r4-r3,r2-2r1,r3-3r1
1 -1 2 1 0
0 0 0 0 0
0 3 0 -4 1
0 0 0 4 0
r2+r3,r4*(1/4),r1-r4
1 -1 2 0 0
0 0 0 0 0
0 3 0 0 1
0 0 0 1 0
r3*(1/3),r1+r3
1 0 2 0 1/3
0 0 0 0 0
0 1 0 0 1/3
0 0 0 1 0
交换 行
1 0 2 0 1/3
0 1 0 0 1/3
0 0 0 1 0
0 0 0 0 0
(行最简形)
列处理得
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 0 0