哈工大版线性代数与空间解析几何课后题答案(6)

a0 0

按第1行展开 0a 01 1

( 1)a ( 1)1 n

00 a

an ( 1)1 n( 1)n 1 1an 2 an an 2.

00 01a0 0a

0 0 00 a0

11 11

(6) Dn 1 1

11111 1 1110 2000 2 000100 2

( 2)n 1 ( 1)n 12n 1. 7．证明

a2

(1) 2a

abb2

1a2

证：2a

a b2b (a b)2 11ab

b2

a b2b2a a ba b 2b2b

c ( 1)c3

112001

3 3

c1 ( 1)c2

a2 abab b2b2

1

a(a b)b(a b)

( 1)

a ba bab

(a b)2 (a b)3

11

a2

(2)

(a 1)2(b 1)2(c 1)2(d 1)2

a2b2c

2

(a 2)2(b 2)2(c 2)2(d 2)2

(a 3)2(b 3)2(c 3)2(d 3)2

a2 4a 4b2 4b 4c 4c 4

2

b2c2d2

0

a2 2a 1b2 2b 1c 2c 1

2

a2 6a 9b2 6b 9c 6c 9

2

证：等式左端

d2

·6·

d2 2d 1d2 4d 4d2 6d 9