大一线性代数练习题五套(带答案)(5)

03P A 00021 00053 12300 , A 1.45800 34600

A2 .A4 A103Q A1,A4 m,n , A A3

04A A , |A| 3,

(1)|2A 1| _________;

(3)|(A*)*| ________;

(5)|5A 1 2A*| _________;

(7)|4A (A*)*| _________.(2)|A*| _________;(4)|(A*) 1| __________;(6)|(2A)*| ________;

11 A (3A)*=04B A 3 , |A| 2, 12 ||.

04Cn , A2 E, B (Aij)n n, Aij |A| aij , B2 E.

04D .

04E A n , :(A ) |A|n 2A.

04F 3 A A

.

04G A n , n ,b ,

0 EP ,T*A A AQ T 1 111 121 A* 113 ,b

A* A ,E n .

(1) PQ;

(2) : Q TA 1 b.

.15.