3.1.1 3.1.2

3.1.1 1 mnAkA(rank)r(A)r(0)=0.1

4r(A)

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.

= +.