07线性代数讲义[1](10)

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

x ¦I ª' .

10 2

~D= 013

231

.

A.D=1A11+0A12+( 2)A13,Ù¥A11

01

( 1)1+3 =2,ÏdD= 12.

23

123

~D= 456 ,¦7A11+8A12+9A13"

789 A.7A11+8A12+9A13=0.

11···1 a1a2···an

2~.y²Dn= a2···a2n2 a1

········· ···

n 1n 1

1 a1a2···ann

b'I ª&¡ n0 % I ª.y².én^VB{,¨n=2 ,w,¤á.#n≤k @ؤá,¨n=k+1

2 13=( 1)

31

= 8,A13=

=

1≤i<j≤n(aj ai),Ù¥n>1.

=

=

=

=

11···1

0a2 a1···an a1

22Dn= ···an ana1 a2 a2a1 0

········· ···

1n 2n 2n 1 0an a2a1···an ana1 2

a2 a1a3 a1···an a1 a(a a)a3(a3 a1)···an(an a1) 22 1 ············ an 2(a a)an 2(a a)···an 2(a a)

31n12123n 11···1 aa3···an 2

(a2 a1)···(an a1)

··· ········· an 2an 2···an 2 23n

(a2 a1)···(an a1)(aj ai)=(aj ai)

2≤i<j≤n

1≤i<j≤n

=m.