07线性代数讲义[1](17)

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

21 23

A. 32 12

333 3

111 1

→ 0 1 45

014 5 4,¤± §|ÃA.

121

4 → 32501

131

5 → 020

2312

124 → 14 510

11 13

1 45 5 ,000 4

3 231

11 13 14 51  Ñy0=

·K1.19

a11x1+a12x2+···+a1nxn=b1 ax+ax+···+ax=b2112222nn2

.

............................................

am1x1+am2x2+···+amnxn=bm¯@o §|'yPÝ A

0···0c1i1

0···00

¯→ 0···00A ······

0···000···00

²vÐ1C C ·······c2,i2···0·······0···0

····

·······c3,i3·······0···0

····

···············cs,is···0

···

···············

,

(I)

(II)

Ù¥c1,i1,···,cs,is ""Ý (II) ¡ F/Ý "

¯=0,@o@Øw,"¯=0.ém^VB{"y².XtyPÝ Ay#A¨m=

1 @Øw,"#m>1.#I "' i1 "òi1 ¥' "£ (P c1,i1)Ïvx I'Ð1g x I I", P^ I¦ ê\ I IòIi1 'I2 £ g 0"Ó ±òIi1 'Ù§£ g 0"y Ä uI I  e'Ý B"dVBb# B dÐ1g g 0···

0··· B→ ····

0···0···

00·0000·00

···c2,i2···0·······0···0

····

···c3,i3·······0···0

····

···········cs,is···0

···

············

,

(III)

¯ ²vÐ1g g (II).2Ù¥c1,i2,···,cs,is ""l A

·K1.20Q·K1.19'PÒe§· kXe@ص

(i)¨is=n+1 § §|ÃA;(ii)¨s=n § §|k A;

(iii)¨s<n § §|kÃê A"d ¡xi1,···,xis gd þ§ ٧ѡ gd þ"