Solve a system of linear equations Ax=kb(adsbygoogle = window.adsbygoogle || []).push({});

A is a matrix with m*n elements,

[tex]A = \left[\stackrel{a_{11}\; \ldots \;a_{1n}}{ \vdots \ \ddots \ \vdots} {a_{m1}\cdots a_{mn} \\} \right][/tex]

[tex] \sum _{j=1} ^{n}a_{ij}=1 ,0\leq a_{ij}\leq1, 1\leq i\leq m,1\leq j \leq n , m > n[/tex]

b is a vector with m*1 elements,

[tex]0 \leq b_{i} \leq 1 \;,\; 1 \leq i \leq m [/tex],

x is the unknown vector with n*1 elements,

[tex]0 \leq x_{j} \leq 1\:,\:1 \leq j \leq n [/tex],

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!

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