将下列矩阵化为行最简阶梯形矩阵

题目

将下列矩阵化为行最简阶梯形矩阵
2 3 -1 5 3 4 -5 7
3 1 2 -7 2 -3 3 2
4 1 -3 6 4 11 -13 16
1 -2 4 -7 7 -2 1 3

答案

r1-3r2,r3-r2,r4+2r2
-7 0 -7 26
3 1 2 -7
1 0 -5 13
7 0 8 -21
r1+r4,r4-7r3
0 0 1 5
3 1 2 -7
1 0 -5 13
0 0 43 -112
r4-43r1
0 0 1 5
3 1 2 -7
1 0 -5 13
0 0 0 -327
r4*(-1/327),r1-5r4,r2+7r4,r3-13r4
0 0 1 0
3 1 2 0
1 0 -5 0
0 0 0 1
r2-2r1,r3+5r1
0 0 1 0
3 1 0 0
1 0 0 0
0 0 0 1
r2-3r3
0 0 1 0
0 1 0 0
1 0 0 0
0 0 0 1
交换行得
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
(2)
r1-r2,r3-2r2
-->
1 7 -8 9
2 -3 3 -2
0 17 -19 20
7 -2 1 3
r2-2r1,r4-7r1
-->
1 7 -8 9
0 -17 19 -20
0 17 -19 20
0 -51 57 60
r3+r2,r4-3r2,r2*(-1/17)
1 7 -8 9
0 1 -19/17 20/17
0 0 0 0
0 0 0 0
r1-7r2
1 0 -3/17 13/17
0 1 -19/17 20/17
0 0 0 0
0 0 0 0