Principles of Mathematics in Operations Research

Solutions 213

(b) Differentiator:

A(n,k) =

0 •

0 •

0-

• 
  


• 0


• 0

n;=i»

0

0

0

0

[B(

0 0 0

0 0

o IlEj-'i o

0 0

0 0 0

n,k)\N(n,h)]->

III

[/„-

0

0

0

0

=n-fc+l l.

-*+i|0]

= [N(n,k)\B(n,k)]

Then,

K{A) = Span{ | Y[i J ei,--- , I J| i J e„_fc+i

V*=l

= Span{ei,.--,en_fc+1}=R"-fc+1.

7e(Ar) = Sp«n<M JJi J efc+x,-- , I JJ i\e„

I \i=l / \j=n-fc+l /

= Span{ek+1,--- , en} = R"-fc+1.

/o\l

0

A/"(i4) = Span < > = Span{ei,--- ,ek} = '.

IW \0/J

M{AT) = {0} , dimM(AT) = 0.