Solve a system of linear equations Ax=kb

[turbulent1]

Solve a system of linear equations Ax=kb
A is a matrix with m*n elements,
$$A = \left[\stackrel{a_{11}\; \ldots \;a_{1n}}{ \vdots \ \ddots \ \vdots} {a_{m1}\cdots a_{mn} \\} \right]$$
$$\sum _{j=1} ^{n}a_{ij}=1 ,0\leq a_{ij}\leq1, 1\leq i\leq m,1\leq j \leq n , m > n$$
b is a vector with m*1 elements,
$$0 \leq b_{i} \leq 1 \;,\; 1 \leq i \leq m$$,
x is the unknown vector with n*1 elements,
$$0 \leq x_{j} \leq 1\:,\:1 \leq j \leq n$$,
k is an arbitrary constant which makes x satisfy the system of equations.
find the unknown vector x.

I think it's not proper to solve the system by finding the pseudo-inverse matrix of A,
because some elements of x are than 0.

Your suggestions are welcome, thanks!

 

[HallsofIvy]

What exactly do you want? You have a general matrix equation, restricted only by the requirement that the sum of each row be 1 (a stochastic matrix?). There is no one solution. How you would solve it, even whether it has a solution, depends strongly on the actual values.

 

[turbulent1]

Thank you professor HallsofIvy for your reply!
The attachment is a pdf file, which contains the data in the equations.

 

[turbulent1]

Could anyone give any hint?