07线性代数讲义[1](13)

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

½n1.17XtD=0,@o §|(I)k Aµx1=D1/D,x2=D2/D,···,xn=Dn/D.

y²(1).ky²x1=D1/D,x2=D2/D,···,xn=Dn/D´(I)'A.Dj=b1A1j+···+bnAnj.òx1=D1/D,x2=D2/D,···,xn=Dn/D \ §|'I §µ

nnn 11

a1j(biAij)a11(D1/D)+a12(D2/D)+···+a1n(Dn/D)=((a1jDj))=1

=n n j=1i=1

1

bi(a1jAij)=n n i=1j=1

1

bi(a1jAij)=j=1n

bi(

n

j=1i=1

i=1j=1

1

a1jAij)=b1D=b1

^Ó ' { ±&µx1=D1/D,x2=D2/D,···,xn=Dn/D÷vI2

§,···,In §.Ïd,§´(I)'A.

(2).Py S.=Xt k(c1,···,cn) ´ §|(I)'A,@U÷v(I)¥'z §.=ai1c1+ai2c2+···+aincn=bi,i=1,2,···,n.· w

a11c1a12···a1n

aca

21122···a2n

c1D=

············

aca

n11n2···ann

a11c1+a12c2a12···a1n

ac+acaa2n òc2¦I2 \I1 211 22222···

=

············

ac+aca

n11n22n2···ann

a11c1+a12c2+···+a1ncna12···a1n

ac+ac+···+acaa2n 2112222nn22···

=···=

············

ac+ac+···+aca

n11n22nnnn2···ann

b1a12···a1n

b 2a22···a2n

= =D1.

············

ba···a

n

n2

nn

u´c1=D1/D,Ó ,c2=D2/D,···,cn=Dn/D.2½n1.18Xtàg §

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

am1x1+am2x2+···+amnxn=0'Xê1 ªD=0,@o(II) k"A.

(II)