07线性代数讲义[1](8)

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

§1.4

1 ª Ðm

½Â1.14D= a11a12···a1n aa 2122···a2n

············ uD¥'Ii1Ij & 'f1

an1an2···ann

ª¡ aij'{fª,P

a11···a1(j 1)a1(j+1)···a1n ···

···············

M= a···a (i 1)1···a(i 1)(j 1)a(i 1)(j+1)(i 1)n ij

a .¿ ¡( 1)i+jMij aij'(i+1)1···a(i+1)(j 1)a(i+1)(j+1)···a(i+1)n

·················· an1···an(j 1)an(j+1)···ann ê{fª,P Aij.

½n1.15D=as1A1+as2As2+···+asnAsn.

y².· Äky²e¡@ص

a11a12···a1n ea¥Øa a22···a2n st¤Q'Ist©Ù¦'£ Ñ´",uD=

a21 ············

=an1an2···ann

astAst.

Xts=1=t.wD= ( 1)τ(i1,i2,···,in)

a1i1···anin=a11 ( 1)τ(i2,··· ,in) a2i2···anin=

aa st a11···a1t···a1n s1··· a11···a1t ············ ····a11A11.é?Û1≤s,t≤n,wD=

as1···ast···asn =( 1)s 1 ····· as 1,1···as ············ 1,t as+1,1···as+1,t a n1···ant···ann

···

······ an1···ant

astas1···as,t 1as,t+1···asn a1t

a·a 11··1,t 1as1t+1···a1n

············ ( 1)s 1+t 1 ········· a s 1,tas 1,1···as 1,t 1as 1,t+1···as 1,n

a,tas+1,1···as+1,t 1a =astAst.

s+1s+1,t+1···as+1,n as+1,1···as+1,t···as+1,n ····················· antan1···an,t 1an,t+1···ann

··asn

··a1n···

··as 1··as+1···

··ann

·····