Question

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
很急急急！求高手帮忙

Answer 1

(1)解: 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