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Math Help - determine variables in rect.matrix;sums known

  1. #1
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    determine variables in rect.matrix;sums known

    i need to determine values of vaiables in 6 x 8 matrix; sums of the variables in horizontal and vertical columns are known; variables in my problem takes values between 16 and 22
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  2. #2
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    Quote Originally Posted by vk kabra View Post
    i need to determine values of vaiables in 6 x 8 matrix; sums of the variables in horizontal and vertical columns are known; variables in my problem takes values between 16 and 22
    How you would do that, and, in fact, whether it is possible depends strongly on what the matrix is! It looks to me like you have 6+ 8= 14 equations to solve but I don't know what those equations are without seeing the matrix!
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  3. #3
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    Lets say the variables are from x1 to x6 in the first row, x7 to x12 in the second row, and similarly continuing till x43 to x48 in the eighth row.

    Its given that x1+x2+x3+x4+x5+x6=S1(known)
    x7+x8+x9+x10+x11+x12=S2(known)
    .
    .
    .
    x43+x44+x45+x46+x45+x47=S8(known)

    Also,

    x1+x7+x13+x19+x25+x31+x37+x43=S9(known)
    and so on...

    Yes, there are 14 equations but the number of variables are 48 in between the given range.

    Is there a way to determine the variables?
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  4. #4
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    No. There will be an infinite number of different matrices that have those sums.
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