07线性代数讲义[1](21)

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

§1.9 5 ' 5Ã'

~α1=(1,0,0),α2=(0,1,0),α3=(0,0,1),β=(2,3,4)· B©β=2α1+3α2+4α3, Ò´β dα1,α2,α3v«Ñ5.,©,Xtk1α1+k2α2+k3α3=0,@o íÑk1=k2=k3=0,ùü þ'9XkXe½Â.

½Â1.21α1,···,αs´Pn¥' | þ,k1,···,ks∈P,¡k1α1+···+

ksαs α1,···,αs' 5|Ü.Xtα=k1α1+···+ksαs,u¡α dα1,···,αs 5LÑ, ¡α ¤α1,···,αs' 5|Ü.

~.α=(2, 3,0),β=(0, 1,2),γ=(0, 7, 4),uγØU&α,β SvÑ.A.XtγU&α,β SvÑ,#γ=k1α+k2β,@o(2, 7, 4)=(2k1, 3k1 2k2,2k2),=

2k1=0

(I) 3k1 k2= 7

2k2= 4100200

S §|(I) dpd {&: 3 1 7 → 0 1 7 →

01 202 4

100

0 1 7 .Ïd §|(I)ÃA,gñ.ÏdγØU&α,β SvÑ.009

dþ~ ±wÑ·K1.22QPn¥,Xtα1=(a11,a21,···,an1),αs=(a1s,a2s,···,ans),γ=(b1,b2,···,bn),@oα1,···,αsQP¥U 5LÑγ , §|

a11x1+a12x2+···+a1sxs=b1 ax+ax+···+ax=b2112222ss2 ···············

an1x1+an2x2+···+ansxs=bn

(I)

QP¥kA.c Ú,γ=k1α1+···+ksαs (k1,···,ks)´(I)'A.

y².XtγU&α1,···,αs SvÑ,@o QP¥'s£ þ(k1,···,ks)¦γ=

a11k1+a12k2+···+a1sks=b1 ak+ak+···+ak=b2112222ss2

k1α1+···+ksαs,=.u´(k1,···,ks)´

···············

an1k1+an2k2+···+ansks=bn

§|(I)'A.