Question

求四阶逆矩阵 要过程

-1 3 -7 10
-7 -3 5 10
3 1 -1 2
1 1 -1 2
要过程撒

Answer 1

这个好麻烦

(A,E)=
-1 3 -7 10 1 0 0 0
-7 -3 5 10 0 1 0 0
3 1 -1 2 0 0 1 0
1 1 -1 2 0 0 0 1

r1-3r4,r2+3r4,r3-r4
-4 0 -4 4 1 0 0 -3
-4 0 2 16 0 1 0 3
2 0 0 0 0 0 1 -1
1 1 -1 2 0 0 0 1

r1+2r3,r2+2r3,r3*(1/2),r4-r3
0 0 -4 4 1 0 2 -5
0 0 2 16 0 1 2 1
1 0 0 0 0 0 1/2 -1/2
0 1 -1 2 0 0 -1/2 3/2

r1+2r2,r2*(1/2),r4+r2
0 0 0 36 1 2 6 -3
0 0 1 8 0 1/2 1 1/2
1 0 0 0 0 0 1/2 -1/2
0 1 0 10 0 1/2 1/2 2

r1*(1/36),r2-8r1,r4-10r1
0 0 0 1 1/36 1/18 1/6 -1/12
0 0 1 0 -2/9 1/18 -1/3 7/6
1 0 0 0 0 0 1/2 -1/2
0 1 0 0 -5/18 -1/18 -7/6 17/6

交换行
1 0 0 0 0 0 1/2 -1/2
0 1 0 0 -5/18 -1/18 -7/6 17/6
0 0 1 0 -2/9 1/18 -1/3 7/6
0 0 0 1 1/36 1/18 1/6 -1/12

所以 A^-1=
0 0 1/2 -1/2
-5/18 -1/18 -7/6 17/6
-2/9 1/18 -1/3 7/6
1/36 1/18 1/6 -1/12

Answer 2

答案如图