同济大学线性代数第六版答案(5)

(4)d c b a 100110011001--- 解 d c b a 10011001

1001---d

c b

a a

b ar r 1001100

1101021---

++=====

d c a ab 101101)1)(1(12--+--=+01011123-+-++=====cd c ad

a a

b d

c c

cd ad ab +-+--=+111)1)(1(23abcd ab cd ad 1 5 证明:

(1)111222

2b b a a b ab

a +(a

b )3; 证明

111222

2

b b a a b ab a +0012222

2

2

2

1213a b a b a a b a ab a c c c c ------=====

a b a b a b a ab 22)1(2

2

2

13-----=+21))((a

b a a b a b +--=(a b )3

(2)y

x z x z y z

y x b a bz ay by ax bx az by ax bx az bz ay bx az bz ay by ax )(33+=+++++++++;

证明

bz ay by ax bx az by ax bx az bz ay bx

az bz ay by ax +++++++++