07线性代数讲义[1](9)

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

yQ· 5y²½n,w

a

11a12···

·········

D= as10···

·········

an1an2···

a1n ···

0 + ···

ann

a11···0···an1a12···as2···an2

···············

a1n

···

asn

···

ann

a11a12···a1n ············

=as1As1+

0

as2···asn ············

an1

an2 ···

a

nn

a11a12···a1n ············

=as1As1+as2As2+

00···ain ············

an1an2···

a

nn

=as1As1+as2As2+···+asnAsn.2

a11a12···a1n

íØ1.16 D= a

21a22···a2n

············ ,u

a

n1an

2···ann

i)adk=i

k1Ai1+·+aknAin=

0k=i;

ii)ads=j

1sA1j+·+ansAnj=0s=j

.

a11 ···

a

(i 1)1y².i)¨i=k ,dUIÐmª &"y#i=k.du

ak1

a(i+1)1

···

a k1

···.

an10, ¡d½n1.15,þª =ak1Ai1+·+aknAin,Ïdi)¤ª=  ØUgI ª' ,Ïdii) di)íÑ.2

a12·········a(i 1)2···ak2···a(i+1)2·········ak2·········an2···á;Ï Ia 1n ··· a(i 1)n a kn a(i+1)n

··· =a kn ··· a nn