Question

线性代数题目，求高手解答！！ 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|

3Q~~

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.