Question

用初等行变换化下列矩阵为行最简形 2 3 1 -3 -7 1 2 0 -2 -4 3 -2 8 3 0 2 -3 7 4 2 大家帮下手解决!谢谢

2 3 1 -3 -7
1 2 0 -2 -4
3 -2 8 3 0
2 -3 7 4 2

Answer 1

r1-2r2,r3-3r2,r4-2r2
0 -1 1 1 1
1 2 0 -2 -4
0 -8 8 9 12
0 -7 7 8 10

r1*(-1),r2-2r1,r3+8r1,r4+7r1
0 1 -1 -1 -1
1 0 2 0 -2
0 0 0 1 4
0 0 0 1 3

r1+r3,r4-r3
0 1 -1 0 3
1 0 2 0 -2
0 0 0 1 4
0 0 0 0 -1

r4*(-1),r1-3r4,r2+2r4,r3-4r4
0 1 -1 0 0
1 0 2 0 0
0 0 0 1 0
0 0 0 0 1

r1<->r2
1 0 2 0 0
0 1 -1 0 0
0 0 0 1 0
0 0 0 0 1

此为行最简形.