07线性代数讲义[1](12)

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

§1.5Gramer{u

yQ· 5?Øn£ §|

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

am1x1+am2x2+···+amnxn=bm

(I)

'A¯K.x1,x2,···,xn&¡ (I)'n þ.

ùpn ±Ø1um.aij∈P,´~ê,§&¡ §|(I)'Xê.b1,b2,···,bn∈P,§ &¡ §|(I)'~ê .

Xtò~êc1,···,cn \ §¥x1,···,xn¦ §|(I)¤á,@o¡ù|ê(c1,c2,···,cn) §|(I)' |A.

Xté?Û |ê(c1,···,cn)∈Pn,§ÑØU÷v §|(I),@o¡ §|QP¥ÃA.

2x+3y=4

~X±eù §|´ÃA'µ

2x+3y=0

Xtb1=0,b2=0,···,bn=0,@o §|£I¤g

a11x1+a12x2+···+a1nxn=0 ax+ax+···+ax=02112222nn ............................................

am1x1+am2x2+···+amnxn=0

(II)

¿ ¡§ àg S §|.Ï (0,0,···,0)´£II¤'A(&¡ 0A),Ïdàg S §|o´kA'.àg S §|Ø"A© Uk "A.~X

x 2y+z=0x+y+z=0

x=1,y=0,z= 1 ´ §' |A.

A S §|' {kxõ,e¡· Ñ «^I ª5¦A' {.=Gramer {.ù« { ¦ §ê þ ê Ó(m=n).

a11a12···a1n a 21a22···a2n

PD= ,

············ a n1an2···ann

ù I ª&¡ §|(I)'XêI ª.Dj D¥Ij d~ê b1,···,bn O& 'I ª.=

a11···a1(j 1)b1a1(j+1)···a1n a 21···a2(j 1)b2a2(j+1)···a2n Dj= .

····················· abnan(j+1)···ann n1···an(j 1)