07线性代数讲义[1](5)

大学线性代数讲义前面有对知识的讲解,后面是习题。便于理解。不想挂科的同学们的必备之物

2 12 213 ~X 110 = 111

312 202

5 1.7D=D.

a11a 12···a 1n a11a12···a1n

a

21a22···a2n a21a22···a2n

y².PD= . ,D=

············ ············

a

an1an2···ann n1an2···ann

τ(i1,i2,···,in)

D=( 1)a1i1···anin,D=( 1)τ(j1,j2,···,jn)a1j1···anjn.d=

'½Â aij=aji.é?Û ü j1,j2,···,jn,-i1,i2,···,in,¦&ji1=1,ji2=2,···,jin=n.w( 1)τ(j1,j2,···,jn)a1j1···anjn

=( 1)τ(j1,j2,···,jn)aj11···ajnn=( 1)τ(j1,j2,···,jn)a1i1···anin=( 1)τ(i1,i2,···,in)a1i1···anin

¤±D=D.

5 1.8¢ 1 ªü1 ,& '#1 ªUCÎÒ.

··············· ···············

at1at2······atn as1as2······asn

y².#I ªD= ··············· ,D1= ··············· .

as1as2······asn at1at2······atn

··············· ···············

yD= D1.dI ª½ÂD1=( 1)τ(i1,···,it,···,is···,in)a1i1···atit···asis···anin

= ( 1)τ(i1,···,is,···,it···,in)a1i1···asis···atit···anin= D.2íØ1.9e1 ªü1 Ó,ud1 ª ".

5 1.10^êk¦±1 ªD', 1& '1 ªD1´D'k .=D1=kD.

y².^êk¦±I ªD'IsI& 'I ªD1.wD1=( 1)τ(i1,i2,···,in)a1i1···(kasis)···anin

=k( 1)τ(i1,i2,···,in)a1i1···asis···anin=kD,

············

a+a a+a ···a+a j1jnj2j2jn j1

5 1.11D= =

············ ············

············ ············ a j1aj2···ajn aj1aj2···ajn + . ············ ············ ············ ············

(dÚn1.6).