[Scilab-users] a linear equation

[fujimoto2005]

This problem is an economic problem. The i-th row of the square constraint
matrix A with m dimension expresses certain economic constraints.
The elements of the constraint matrix are either 0 or 1.
Suppose the rank of A is r and by changing the row number a_1, ..., a_r are
linearly independent. 
I guess the coefficient cj (1 ≤ j ≤ r) in a_i = c1 * a_1 + ... cr * a_r for
any m>=i> r is found to be 0, -1, 1 for some economic reasons.
I would like to find such a_1, ..., a_r pairs.

The following matrix is the constraint matrix which I am dealing with.

A=zeros(27,27)

A(1,10)=1
A(2,5)=1
A(3,14)=1
A(4,23)=1
A(5,9)=1
A(6,18)=1
A(7,27)=1
A(8,17)=1
A(9,1)=0,A(9,18)=1
A(10,2)=1,A(10,3)=1
A(11,4)=1,A(11,5)=1,A(11,6)=1
A(12,7)=1,A(12,8)=1,A(12,9)=1
A(13,10)=1,A(13,11)=1,A(13,12)=1
A(14,13)=1,A(14,14)=1,A(14,15)=1
A(15,19)=1,A(15,20)=1,A(15,21)=1
A(16,22)=1,A(16,23)=1,A(16,24)=1
A(17,1)=0,A(17,25)=1,A(17,26)=1,A(17,27)=1
A(18,4)=1,A(18,7)=1
A(19,2)=1,A(19,5)=1,A(19,8)=1
A(20,10)=1,A(20,13)=1,A(20,16)=1
A(21,11)=1,A(21,14)=1,A(21,17)=1
A(22,19)=1,A(22,22)=1,A(22,25)=1
A(23,1)=0,A(23,20)=1,A(23,23)=1,A(23,26)=1
A(24,4)=1,A(24,7)=1
A(25,2)=1,A(25,5)=1,A(25,8)=1
A(26,10)=1,A(26,13)=1,A(26,16)=1
A(27,20)=1,A(27,23)=1,A(27,26)=1

Best regards.



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