🚀 go-pugleaf

 AX=B, A=[a1 a2 a3 ... an], X=[x1 x2 x3 ...xn]' , a's and B are (mx1) vectors
                               x's are scalars.
 Known: only a1
 Sought: x1

 The problem seems ridiculous, but it does make sense and is important.
 If a1 is orthogonal to other a's,  the problem is perfectly soluble.
              x1=a1\B=a1^{+}B
 If a1 is linearly related to others, it's absolutely insoluble.

 There must be somthing between the extremes, especially if we add some
 constraints. The  physical meaning of my problem requires that nothing be
 negative, none of the elements of a's. x's and B. Thus, the problem becomes
      AX <= B,  A=[a1 a2 a3 ... an], X=[x1 x2 x3 ...xn]' ,
                     a's and B are (mx1) vectors
      rank(A)=n, A is well conditioned(not orthogonal, however).
                 All elements      of A and B are non-negative.
      Sought: X, which is all positive.

I don't know how to start the analysis.
Any advice/hints/help/references will be highly appreciated.
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