Question

求逆矩阵 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
r1r2
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