用初等变换法求下列矩阵的逆矩阵，求解

Question

如题所述

Answer 1

用初等行变化求矩阵的逆矩阵,
即用行变换把矩阵(A,E)化成(E,B)的形式,那么B就等于A的逆
在这里
(A,E)=
-1 1 1 1 1 0 0 0
-1 -1 1 1 0 1 0 0
-1 -1 -1 1 0 0 1 0
-1 -1 -1 -1 0 0 0 1 r1+r4, r2+r4, r4-r3
～
-2 0 0 0 1 0 0 1
-2 -2 0 0 0 1 0 1
-1 -1 -1 1 0 0 1 0
0 0 0 -2 0 0-1 1 r2-r1 ,r1/(-2) ,r2/(-2) ,r4/(-2)
~
1 0 0 0 -1/2 0 0 -1/2
0 1 0 0 1/2 -1/2 0 0
-1 -1 -1 1 0 0 1 0
0 0 0 1 0 0 1/2 -1/2 r3+r1,r3+r2,r3-r4 ,r3*(-1)
~
1 0 0 0 -1/2 0 0 -1/2
0 1 0 0 1/2 -1/2 0 0
0 0 1 0 0 1/2 -1/2 0
0 0 0 1 0 0 1/2 -1/2
这样就已经通过初等行变换把(A,E)～(E,A^-1)
于是得到了原矩阵的逆矩阵就是
-1/2 0 0 -1/2
1/2 -1/2 0 0
0 1/2 -1/2 0
0 0 1/2 -1/2本回答被提问者和网友采纳