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andreass
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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?