线性代数第二章 ppt 上传

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1、1.n;2.;n3.;4...a11a121.x1,x21.1.a21a22=a11a22−a12a21,a11x1+a12x2=b1,,,,(1)a21x1+a22x2=b2,,.

2、aij(i,j=1,2)ij.a11,a12,a21,a22,b1,b2.a11x1+a12x2=b1a11a122.a21x1+a22x2=b2,D=a21a22,2..a11a22−a12a21=0,D1=b1a12,D2=a11b1,D.b2a22a21b2a22b1−a12b2x1=,(2)a11a22−a12a213.D=0,,D1D2a11b

3、2−a21b1x1=D,x2=D.(4)x2=.(3)a11a22−a12a214.(4)(2)(3),(4)3.(2)(3)(1).(a11a22−a12a21=0).(4)(2),(3).(Cramer).1.1.2x1+3x2=5,.n−3x1+x2=3,n,2...

4、23D==2+9=11=0,1.2.nA=(aij)n×nij−31,n−15325,aij,A(i,j).D1=31=−4,D2=−33=21,0123.2.1.3A=1−12,a11,a21,a32231D14D221x1==−,x2==..D11D11−12124.3.:A(1,1)=31,A(2,1)=31,A(3,2)=

5、.,02.12,.4.A=[a](),.det(A)=a.A=(aij)2×22,n1.det(A(i,j))ai,j(),.2.a˜=(−1)i+jdet(A(i,j))a(iji,j1.3.nA=(aij)n×n,).a11a12···a1nTaa··

6、·a3.˜aj=(˜a1j,···,a˜nj)Adet(A)=21222n,A.jT············aj=(a1j,···,anj).an1an2···anndet(A)=a11a˜11+···+an1a˜n12.=(˜a,a˜,···,a˜)(a,a,···,a)T=˜aTa=aT˜a.1121n11121n11111n=1,A=(a11),det(A)=a11;4.,.n>1,det(A)=a(−1)1+1d

7、et(A(1,1))+a(−1)2+1det(A(2,1))5.1.j,1121+···+an1(−1)n+1det(A(n,1))j.n=a(−1)k+1det(A(k,1)),k16..,.k=1,A(k,1)ak1.,:,80−11.2.241.a11a12a13−3−211.

8、a21a22a23a31a32a332.:1+12+13+1=32+4+0−12−(−16)−