Question

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

Answer 1

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