■等面単体の体積(その92)

9A=|0,3,3+1,3,3|

   |3,0,3+0,4,3|

   |4,3,0+0,3,3|

   |3,4,3+0,0,3|

   |3,3,3+0,3,0|

|0,3,3,3,3|+|0,3,1,3,3|

|3,0,3,4,3| |3,0,0,4,3|

|4,3,0,3,3| |4,3,0,3,3|

|3,4,3,0,3| |3,4,0,0,3|

|3,3,3,3,0| |3,3,0,3,0|

|0,3,3,3,3|+|0,3,3,0,3|+|0,3,1,3,3|

|3,0,3,3,3| |3,0,3,1,3| |3,0,0,4,3|

|4,3,0,3,3| |4,3,0,0,3| |4,3,0,3,3|

|3,4,3,0,3| |3,4,3,0,3| |3,4,0,0,3|

|3,3,3,3,0| |3,3,3,0,0| |3,3,0,3,0|

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|0,3,3,3,3|

|3,0,3,3,3|

|4,3,0,3,3|

|3,4,3,0,3|

|3,3,3,3,0|

 まず,第1行を他の行から引いて

|0,3,3,3,3|

|3,−3,0,0,0|

|4,0,−3,0,0|

|3,1,0,−3,0|

|3,0,0,0,−3|

さらに第2列〜第n列を第1列に加えれば

  |12,3,3,3,3|

  |0,−3,0,0,0|

  |1,0,−3,0,0|

  |0,1,0,−3,0|

  |0,0,0,0,−3|

のように上三角行列式にならない.

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