3.1.1 3.1.2
3.1.1 1 mnAkA(rank)r(A)r(0)=0.1
Akr(A)k.r(A)=kAkAkk().Amn r(A)min(m,n) r(A)=r(A')Ar(A)=0.
Anr(A)ndet(A)0 r(A)=n.
3.1.2 2 mn 1. k+1k(k=1,2,,m-1). 2. .
10. 2 AB
1 mnA.1 mnA.2 AmnBmnr(BA)=r(AB)=r(A).3 mnA A=PNQ N= r(A)=r
.
2 mnA.3
.
1BA r(A)=r(B)=3.
Ar(A).
3.2.1 3.2.2
3.2.1 3 nAx=b1r(A)r()2r(A)=r()=n3r(A)=r()n.
3.2.2 1. r(A)r().r(A)r().2. r(A)=r().A.
3. r(A)=r()=rrn-r An-r.
1
4 1Ax=br(A)=r(A|b) 2nAx=0r(A)n.
3.3.1 3.3.2 3.3.3 3.3.4
3.3.1 3 k k .
1
.
.
3.3.2 5 k2.6 .
1 .2 .3 .
4 .5 .6 nkkn .
.
3.3.3 4 ()12 .2
.
A
124 .
5 r..
3.3.4 6 mn
A .
7 Amn Ar(A) Ar(A) = =r(A)
3.4.1 3.4.2
3.4.1 1.2.3..
7 Ax=0 Ax=01Ax=0 2 .8 n-rrn-r.
3.4.2 Ax=b0Ax=0Ax=0Ax=bAx=bAx=0Ax=bAx=0
Ax=b = +Ax=0. Ax=bAx=0.1 .
1 . B
2.
= +.
Top Related