Question

用初等行变换把以下矩阵化为行最简形矩阵:

用初等行变换把以下矩阵化为行最简形矩阵:r1: 2 3 1 -3 -7
r2: 1 2 0 -2 -4
r3: 3 -2 8 3 0
r4: 2 -3 7 4 3

拜托了

Answer 1

A =
2 3 1 -3 -7
1 2 0 -2 -4
3 -2 8 3 0
2 -3 7 4 3
交换第1,2行
A =
1 2 0 -2 -4
2 3 1 -3 -7
3 -2 8 3 0
2 -3 7 4 3
r2-2r1,r3-3r1,r4-2r1
A =
1 2 0 -2 -4
0 -1 1 1 1
0 -8 8 9 12
0 -7 7 8 11
r2 = -r2
A =
1 2 0 -2 -4
0 1 -1 -1 -1
0 -8 8 9 12
0 -7 7 8 11
r3+8r2,r4+7r2
A =
1 2 0 -2 -4
0 1 -1 -1 -1
0 0 0 1 4
0 0 0 1 4
r4-r3
A =
1 2 0 -2 -4
0 1 -1 -1 -1
0 0 0 1 4
0 0 0 0 0
r1+2r3,r2+r3
A =
1 2 0 0 4
0 1 -1 0 3
0 0 0 1 4
0 0 0 0 0
r1-2r2
A =
1 0 2 0 -2
0 1 -1 0 3
0 0 0 1 4
0 0 0 0 0