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## Homework Statement

Given:

a>=b>=c>=0,

d>=e>=f>=0,

a>=d

a+b>=d+e

a+b+c=d+e+f

a,b,c,d,e,f belong to Real numbers

Prove that d, e, f can be expressed as linear combinations of a, b and c in such way:

d=(c1+c2)*a+(c3+c4)*b+(c5+c6)*c

e = (c1+c6)*a+(c2+c4)*b+(c3+c5)*c

f=(c1+c3)*a+(c2+c5)*b+(c4+c6)*c

c1, c2, c3, c4, c5, c5 >=0

## The Attempt at a Solution

Only thing I can prove is that c1+c2+c3+c4+c5+c6 = 1 (using a+b+c=d+e+f).

I think I need to find some expression for b, to be able do something, but I'm not sure.

Any suggestions?