将矩阵化为阶梯型

将矩阵化为阶梯型
将矩阵化为阶梯型

将矩阵化为阶梯型
(1) A=
1 1 2 -1
2 1 1 -1
2 2 1 2
r3-r2,r2-2r1
1 1 2 -1
0 -1 -3 1
0 1 0 3
r3+r2
1 1 2 -1
0 -1 -3 1
0 0 3 2
(2) A=
1 1 5 -1
1 1 -2 3
3 -1 8 1
1 3 -9 7
r2-r1,r3-3r1,r4-r1
1 1 5 -1
0 0 -7 4
0 -4 -7 4
0 2 -14 8
r3-r2,r4-2r2
1 1 5 -1
0 0 -7 4
0 -4 0 0
0 2 0 0
r3+2r4
1 1 5 -1
0 0 -7 4
0 0 0 0
0 2 0 0
交换行
1 1 5 -1
0 2 0 0
0 0 -7 4
0 0 0 0
(3) A=
1 -1 1 -1
2 -1 0 1
3 1 2 -1
4 1 3 2
r4-r1-r3,r2-2r1,r3-3r1
1 -1 1 -1
0 1 -2 3
0 4 -1 2
0 1 0 4
r2-r4,r3-4r4
1 -1 1 -1
0 0 -2 -1
0 0 -1 -14
0 1 0 4
r2-2r3
1 -1 1 -1
0 0 0 27
0 0 -1 -14
0 1 0 4
交换行
1 -1 1 -1
0 1 0 4
0 0 -1 -14
0 0 0 27