Question

线性代数题目,设A=【2 0 0 0】 1 2 0 0 0 0 3 0 0 0 1 3 求A的逆矩阵,|A的八次方|

Answer 1

2 0 0 0

1 2 0 0

0 0 3 0

0 0 1 3

矩阵分块为

B 0

0 C

B =

2 0

1 2

B^-1 =

1/2 0

-1/4 1/2

C=

3 0

1 3

C^-1 =

1/3 0

-1/9 1/3

A^-1 =

B^-1 0

0 C^-1

=

1/2 0 0 0

-1/4 1/2 0 0

0 0 1/3 0

0 0 -1/9 1/3

|A| = |B||C| = 4* 9 = 36

|A^8| = |A|^8 = 36^8.