Question

求下列矩阵的逆矩阵,有两题.

Answer 1

(1).(A,E)=

1 2 3 1 0 0

2 2 1 0 1 0

3 4 3 0 0 1

初等行变换为

1 2 3 1 0 0

0 -2 -5 -2 1 0

0 -2 -6 -3 0 1

初等行变换为

1 2 3 1 0 0

0 -2 -5 -2 1 0

0 0 -1 -1 -1 1

初等行变换为

1 2 0 -2 -3 3

0 -2 0 3 6 -5

0 0 1 1 1 -1

初等行变换为

1 0 0 1 3 -2

0 -2 0 3 6 -5

0 0 1 1 1 -1

初等行变换为

1 0 0 1 3 -2

0 1 0 -3/2 -3 5/2

0 0 1 1 1 -1

则 A^(-1)=

1 3 -2

-3/2 -3 5/2

1 1 -1.

(2).(A,E)=

1 0 1 1 0 0

2 1 0 0 1 0

-3 2 -5 0 0 1

初等行变换为

1 0 1 1 0 0

0 1 -2 -2 1 0

0 2 -2 3 0 1

初等行变换为

1 0 1 1 0 0

0 1 -2 -2 1 0

0 0 2 7 -2 1

初等行变换为

1 0 0 -5/2 1 -1/2

0 1 0 5 -1 1

0 0 1 7/2 -1 1/2

则 A^(-1)=

-5/2 1 -1/2

5 -1 1

7/2 -1 1/2