I have a personal problem I want to solve. I have a system of linear inequalities with 97 unknowns and 150000 ineqaulities, I think formal notation of the problem should be something like this [ x 00000101 ⋯ x 00000197 ⋮ ⋱ ⋮ x 15000001 ⋯ x 15000097 ] × [ y 1 ⋮ y 97 ] = [ z 1 ⋮ z 150000 ] ∀ z ∈ { z i | i ∈ [ 1 , 150000 ] } , z i &gt; 0We also know that ∀ x ∈ leftmost matrix x ∈ { − 1 , 0 , 1 } and there is exacly 5 1s and 5 −1's in every row in leftmost matrix. So, each row sums up to 0.What I want to do is to determine if I can order yi's and if so, I want to find an algorithm to order them.

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I have a personal problem I want to solve. I have a system of linear inequalities with 97 unknowns and 150000 ineqaulities, I think formal notation of the problem should be something like this      [                                        x                      00000101                                    ⋯                                      x                      00000197                                                ⋮                          ⋱                          ⋮                                                  x                      15000001                                    ⋯                                      x                      15000097                                ]    ×      [                                        y            1                                                ⋮                                                  y                      97                                ]    =      [                                        z            1                                                ⋮                                                  z                      150000                                ]    ∀  z  ∈      {          z      i          |    i    ∈    [    1    ,    150000    ]    }    ,      z    i    &amp;gt;  0We also know that   ∀  x  ∈ leftmost matrix   x  ∈      {    −    1    ,    0    ,    1    }   and there is exacly 5 1s and 5 −1&#039;s in every row in leftmost matrix. So, each row sums up to 0.What I want to do is to determine if I can order yi&#039;s and if so, I want to find an algorithm to order them.

Marco Meyer · Accepted Answer

A couple of questions: 1. Does       x      00000709    =  1 represent that player 9 was playing for (lacking a better name) the &#039;home team&#039; in match number 7,       x      00000709    =  −  1 that he/she was playing for the &#039;away team&#039; in match number 7 and       x      00000709    =  0 represents that he/she wasn&#039;t playing at all. 2. Does       z      000005    &amp;gt;  0 represent that the home team won match 5,       z      000005    &amp;lt;  0 that the away won match 5 and       z      000005    =  0 that it was a draw.3. Does       y      25   represent the skills of player 25 (the more positive the number the better the player&#039;s skill)?

Kendall Oneill · Accepted Answer

x      00000709    =  1 represents player 9 was playing for winning side in match 7.       x      00000709    =  −  1 was playing for loser side in match 7. A player with value 0 wasn&#039; playing in that game. So that each row gives you an inequality such that sum of winning team&#039;s values minus sum of losing teams values is       z    i   which is bigger than zero. There is no draws in this game.       y      25   means the skill level of player 25, and the bigger is the better.

I have a personal problem I want to solve. I have a system of linear inequalities with 97 unknowns a

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