Principles of Mathematics in Operations Research

212 Solutions

Fig. S.3. The fundamental cycle defined by edge 10 in Problem2.1

Ax = b, x > 0 using a standard simplex algorithm over GF(2), we will get the network simplex method.

2.2 (a)

4(5,2) =

00 00 00 00

20 0 0 06 0 0 0 0 12 0 00 0 20

[N\B]

where

UB =

[B\N] = \UB\UN] -)• [h\VN]

= 04x2, VN =

20 0 0' 06 0 0 0 0 12 0 00 0 20

, uN =

"0 0" 00 00 00

00 00 00 00

= 04x2-

Then,

TZ(A) = Span {2ei,6e2,12e3,20e4} = Span {e±, e2, e%, e^} = R^4.

The rank of A(n, k) is r = 4.

1Z(AT) = Span {2e3,6e4,12e5,20ee} = Span{e3,e4,e$,eQ} = R^4.

Af(A) = Span <

if

1 ) 0

(^0 0)
0
I Voy
1
1
(o)
1
0
0
0
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