Question

求逆矩阵 详解 在线等 急！！

求
2 1 7
5 3 -1
-4 -3 2
的逆矩阵

Answer 1

解: (A,E) =
2 1 7 1 0 0
5 3 -1 0 1 0
-4 -3 2 0 0 1

r2-3r1,r3+3r1
2 1 7 1 0 0
-1 0 -22 -3 1 0
2 0 23 3 0 1

r1+2r2,r3+2r2
0 1 -37 -5 2 0
-1 0 -22 -3 1 0
0 0 -21 -3 2 1

r2*(-1),r3*(-1/21)
0 1 -37 -5 2 0
1 0 22 3 -1 0
0 0 1 1/7 -2/21 -1/21

r1+37r3,r2-22r3
0 1 0 2/7 -32/21 -37/21
1 0 0 -1/7 23/21 22/21
0 0 1 1/7 -2/21 -1/21

r1<->r2
1 0 0 -1/7 23/21 22/21
0 1 0 2/7 -32/21 -37/21
0 0 1 1/7 -2/21 -1/21

A^-1 =
-1/7 23/21 22/21
2/7 -32/21 -37/21
1/7 -2/21 -1/21

Answer 2

用matlab

Answer 3

A^(-1)=(1/|A|)×A* A^(-1)指A的-1次方
|A|=-21
A*=3 23 -22
6 32 -37
-3 -2 1
剩下的就是乘一下了。