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  1. Nov 26, 2008 #1
    Solve a system of linear equations Ax=kb
    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!

    Attached Files:

    • 1242.bmp
      File size:
      28.9 KB
  2. jcsd
  3. Nov 26, 2008 #2


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    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.
  4. Nov 26, 2008 #3
    Thank you professor HallsofIvy for your reply!
    The attachment is a pdf file, which contains the data in the equations.

    Attached Files:

  5. Dec 9, 2008 #4
    Could anyone give any hint?
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