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Subject: Re: Linear Combination
Date: Thu, 18 Dec 2008 03:03:03 +0000 (UTC)
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"je w" <wangjing_sg@hotmail.com> wrote in message <giccbq$cnf$1@fred.mathworks.com>...
> ........
> Yes both the coefficients for linear combinations and the elements of the array are *integers*; however, we are limiting the array to around 9 elements at most (the example array has 5 elements) in this case, hence, we are expecting a finite number of combinations. 
> .........

  I believe when John said "infinitely many such linear combinations" he was referring to the fact that if you allow your integer coefficients to have either sign (as he stated,) then any given linear combination of two terms can be replaced by infinitely many other possible combinations of the same two values.  For example, suppose your two values are 15 and 24 and you are looking for a linear combination of them such that c1*15+c2*24 = 93.  One solution is c1 = 3 and c3 = 2.  However another is c1 = -5 and c2 = 7.  Yet another is c1 = -13 and c3 = 12, and there are infinitely more that follow this same pattern, c1 dropping or increasing by 8's and c2 changing in the opposite direction by 5's.  Is it possible you had only positive-valued coefficients in mind when you spoke of "a finite number of combinations"?

Roger Stafford