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0

$begingroup$

I have a system of equations that I am trying to approx. an answer to. I don't do any high level mathematics, so excuse any formatting errors.

Find every team's individual match score. vars = $teams*matches$

Each match has 3 teams. The total score for each match is known.

Each team has 12 matches. The total score for each team is known.

The total number of teams and matches is known, and the answers are all integers.

I have setup a matrix as follows:

$ M_iT_j =$ Match i, Team j

$ sum T_j$ = Sum of Team j

$ sum M_i$ = Sum of Match i

$beginbmatrix
0 * M_1T_1 & 1 * M_2T_1 & 1 * M_3T_1 & dots & 1 * M_12T_1 & sum T_1 \
1 * M_1T_2 & 1 * M_2T_2 & 0 * M_3T_1 & dots & 1 * M_12T_2 & sum T_2 \
1 * M_1T_3 & 0 * M_2T_3 & 1 * M_3T_1 & dots & 1 * M_12T_3& sum T_3\
1 * M_1T_4 & 1 * M_2T_4 & 1 * M_3T_1 & dots & 0 * M_12T_4& sum T_4\
dots \
sum M_1 & sum M_2 & sum M_3 & dots & sum M_12 & sumlimits_i=1^12 M_i
endbmatrix$

Obviously you cannot "solve" this, but I am using python to approximate an answer using the least-squares solution.

I don't know how to layout the matrix to make this a solvable system of equations. Does it need to be M*T long? Any advice would be appreciated.

Please comment if any clarification is needed.

matrices systems-of-equations matrix-equations

share|cite|improve this question

asked Mar 10 at 19:34

PLZHELPPLZHELP

213

$endgroup$

add a comment | 

0

$begingroup$

I have a system of equations that I am trying to approx. an answer to. I don't do any high level mathematics, so excuse any formatting errors.

Find every team's individual match score. vars = $teams*matches$

Each match has 3 teams. The total score for each match is known.

Each team has 12 matches. The total score for each team is known.

The total number of teams and matches is known, and the answers are all integers.

I have setup a matrix as follows:

$ M_iT_j =$ Match i, Team j

$ sum T_j$ = Sum of Team j

$ sum M_i$ = Sum of Match i

$beginbmatrix
0 * M_1T_1 & 1 * M_2T_1 & 1 * M_3T_1 & dots & 1 * M_12T_1 & sum T_1 \
1 * M_1T_2 & 1 * M_2T_2 & 0 * M_3T_1 & dots & 1 * M_12T_2 & sum T_2 \
1 * M_1T_3 & 0 * M_2T_3 & 1 * M_3T_1 & dots & 1 * M_12T_3& sum T_3\
1 * M_1T_4 & 1 * M_2T_4 & 1 * M_3T_1 & dots & 0 * M_12T_4& sum T_4\
dots \
sum M_1 & sum M_2 & sum M_3 & dots & sum M_12 & sumlimits_i=1^12 M_i
endbmatrix$

Obviously you cannot "solve" this, but I am using python to approximate an answer using the least-squares solution.

I don't know how to layout the matrix to make this a solvable system of equations. Does it need to be M*T long? Any advice would be appreciated.

Please comment if any clarification is needed.

matrices systems-of-equations matrix-equations

share|cite|improve this question

asked Mar 10 at 19:34

PLZHELPPLZHELP

213

$endgroup$

add a comment | 

$begingroup$

I have a system of equations that I am trying to approx. an answer to. I don't do any high level mathematics, so excuse any formatting errors.

Find every team's individual match score. vars = $teams*matches$

Each match has 3 teams. The total score for each match is known.

Each team has 12 matches. The total score for each team is known.

The total number of teams and matches is known, and the answers are all integers.

I have setup a matrix as follows:

$ M_iT_j =$ Match i, Team j

$ sum T_j$ = Sum of Team j

$ sum M_i$ = Sum of Match i

$beginbmatrix
0 * M_1T_1 & 1 * M_2T_1 & 1 * M_3T_1 & dots & 1 * M_12T_1 & sum T_1 \
1 * M_1T_2 & 1 * M_2T_2 & 0 * M_3T_1 & dots & 1 * M_12T_2 & sum T_2 \
1 * M_1T_3 & 0 * M_2T_3 & 1 * M_3T_1 & dots & 1 * M_12T_3& sum T_3\
1 * M_1T_4 & 1 * M_2T_4 & 1 * M_3T_1 & dots & 0 * M_12T_4& sum T_4\
dots \
sum M_1 & sum M_2 & sum M_3 & dots & sum M_12 & sumlimits_i=1^12 M_i
endbmatrix$

Obviously you cannot "solve" this, but I am using python to approximate an answer using the least-squares solution.

I don't know how to layout the matrix to make this a solvable system of equations. Does it need to be M*T long? Any advice would be appreciated.

Please comment if any clarification is needed.

matrices systems-of-equations matrix-equations

share|cite|improve this question

asked Mar 10 at 19:34

PLZHELPPLZHELP

213

$endgroup$

share|cite|improve this question

asked Mar 10 at 19:34

PLZHELPPLZHELP

213

share|cite|improve this question

asked Mar 10 at 19:34

PLZHELPPLZHELP

213

asked Mar 10 at 19:34

PLZHELPPLZHELP

213

asked Mar 10 at 19:34

PLZHELPPLZHELP

213