Question

求伴随矩阵的逆矩阵？

Answer 1

逆矩阵A^(-1)=A*/|A|
A*是伴随矩阵，|A|是行列式的值
A*=
A11 A21 A31 A41
A12 A22 A32 A42
A13 A23 A33 A43
A14 A24 A34 A44

A11=1×(-1)^(1+1)×5×4×1=20,
A12=-12,A13=A14==A23=A24=A31=A32=A41=A42=A34=0
A21=-8,A22=4,A33=1,A43=-6,A44=-4
所以
A*=
20 -8 0 0
-12 4 0 0
0 0 1 -6
0 0 0 -4
所以
A^(-1)=(-1/4)×A*=
-5 2 0 0
3 -1 0 0
0 0 1/4 3/2
0 0 0 1