大一线性代数练习题五套(带答案)(2)

01H A,B n , , ( ).

(A)AB O A O B O;

(B)|A| 0 A O;

(C)|AB| 0 |A| 0 |B| 0;

(D)A E |A| 1.

01I 1 A n , A 3, A _________.

3 A 3 2 ,B 2 , , , 2, 3 3 , 2 3 3 01J

|A| 24,|B| 3, |A B|.

01K A n , AAT E,|A| 0. |A E|.

01L (1,0, 1)T, A T. |aE An|, E 3 ,n .

01M A (aij) n ,Aij aij , A ,

A22A23 A2n

A32A33 A3n a11|A|n 2 |D|

An2An3 Ann

01N A n , A , (A B)2 E,

(E A 1BT)T(E BA 1) 1.

01O A n ,B n , A B2 .

01P A,B n , A B E. :AB BA.

01Q A,B n ,A2 A,B2 B,(A B)2 A B,

AB O.

01R A2 E, A . A,B , : AB A B ( AB BA).

.10.