用初等变换法求下列矩阵的逆矩阵：{1 2 -1 ,3 1 0,-1 0 -2}

题目

用初等变换法求下列矩阵的逆矩阵：{1 2 -1 ,3 1 0,-1 0 -2}
用初等变换法求下列矩阵的逆矩阵：{1 2 -1
,3 1 0,-1 0 -2}

答案

A :E E :A(^-1)
1 2 -1 1 0 0
3 1 0 0 1 0 r2-r1*3
-1 0 -2 0 0 1 r3+r1
1 2 -1 1 0 0
0 -5 3 -3 1 0 r2+r3*3
0 2 -1 1 0 1
1 2 -1 1 0 0 r1+r2*(-1)
0 1 0 0 1 3
0 2 -1 1 0 1 r3 +r2*(-2)
1 0 -1 1 -1 -3 r1-r3
0 1 0 0 1 3
0 0 -1 0 -2 -5
1 0 0 1 1 2
0 1 0 0 1 3
0 0 -1 0 -2 -5 r3*(-1)
1 0 0 1 1 2
0 1 0 0 1 3
0 0 1 0 2 5
∴A^(-1)=
1 1 2
0 1 3
0 2 5