Mixing
Pivoting Proof on a Canonical Maximum Tableau
$begingroup$
Problem in Question
For this problem, we are supposed to prove that pivoting on $a_{ij}$ in a canonical maximum tableau is equivalent to solving the $i^{th}$ equation of the tableau for the $j^{th}$ variable and replacing every occurrence of this variable in the other equations of the tableau by the resulting expression.
For my proof, I used the entry $a_{22}$ as an example and did the respective algebra and pivoting to prove that they result in identical final expressions. However, from my knowledge of proofs, if I am asked to prove for $a_{ij}$, it means that I must prove it for ALL variables.
I am wondering how to do this. I am not sure where to start.
linear-programming
edited Feb 1 at 11:01
YuiTo Cheng
2,3694937
asked Feb 1 at 10:46
SeePlusPlusSeePlusPlus
12
$endgroup$
add a comment |
$begingroup$
Problem in Question
For this problem, we are supposed to prove that pivoting on $a_{ij}$ in a canonical maximum tableau is equivalent to solving the $i^{th}$ equation of the tableau for the $j^{th}$ variable and replacing every occurrence of this variable in the other equations of the tableau by the resulting expression.
For my proof, I used the entry $a_{22}$ as an example and did the respective algebra and pivoting to prove that they result in identical final expressions. However, from my knowledge of proofs, if I am asked to prove for $a_{ij}$, it means that I must prove it for ALL variables.
I am wondering how to do this. I am not sure where to start.
linear-programming
edited Feb 1 at 11:01
YuiTo Cheng
2,3694937
asked Feb 1 at 10:46
SeePlusPlusSeePlusPlus
12
$endgroup$
add a comment |
$begingroup$
Problem in Question
For this problem, we are supposed to prove that pivoting on $a_{ij}$ in a canonical maximum tableau is equivalent to solving the $i^{th}$ equation of the tableau for the $j^{th}$ variable and replacing every occurrence of this variable in the other equations of the tableau by the resulting expression.
For my proof, I used the entry $a_{22}$ as an example and did the respective algebra and pivoting to prove that they result in identical final expressions. However, from my knowledge of proofs, if I am asked to prove for $a_{ij}$, it means that I must prove it for ALL variables.
I am wondering how to do this. I am not sure where to start.
linear-programming
edited Feb 1 at 11:01
YuiTo Cheng
2,3694937
asked Feb 1 at 10:46
SeePlusPlusSeePlusPlus
12
$endgroup$
Problem in Question
For this problem, we are supposed to prove that pivoting on $a_{ij}$ in a canonical maximum tableau is equivalent to solving the $i^{th}$ equation of the tableau for the $j^{th}$ variable and replacing every occurrence of this variable in the other equations of the tableau by the resulting expression.
For my proof, I used the entry $a_{22}$ as an example and did the respective algebra and pivoting to prove that they result in identical final expressions. However, from my knowledge of proofs, if I am asked to prove for $a_{ij}$, it means that I must prove it for ALL variables.
I am wondering how to do this. I am not sure where to start.
linear-programming
linear-programming
edited Feb 1 at 11:01
YuiTo Cheng
2,3694937
asked Feb 1 at 10:46
SeePlusPlusSeePlusPlus
12
edited Feb 1 at 11:01
YuiTo Cheng
2,3694937
asked Feb 1 at 10:46
SeePlusPlusSeePlusPlus
12
edited Feb 1 at 11:01
YuiTo Cheng
2,3694937
edited Feb 1 at 11:01
YuiTo Cheng
2,3694937
edited Feb 1 at 11:01
YuiTo Cheng
2,3694937
2,3694937
asked Feb 1 at 10:46
SeePlusPlusSeePlusPlus
12
asked Feb 1 at 10:46
SeePlusPlusSeePlusPlus
12
asked Feb 1 at 10:46
SeePlusPlusSeePlusPlus
12
12
add a comment |
add a comment |
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