■等面単体の体積(その232)
n=5のとき,α^2Aの
|0,5,8,9,8,5,α|
|5,0,5,8,9,8,α|
|8,5,0,5,8,9,α1
|9,8,5,0,5,8,α1
|8,9,8,5,0,5,α|
|5,8,9,8,5,0,α|
|α,α,α,α,α,α,0|
第1行を他の行から引いて
=|0, 5, 8, 9, 8, 5, α|
|5,−5,−3,−1, 1, 3, 0|
|8, 0,−8,−4, 0, 4, 01
|9, 3,−3,−9,−3, 3, 01
|8, 4, 0,−4,−8, 0, 0|
|5, 3, 1,−1,−3,−5 ,0|
|α,α−5,α−8,α−9,α−8,α−5,−α|
第2列〜第n列を第1列に加えれば
=|35+α,5,8, 9, 8, 5, α|
| 0,−5,−3,−1, 1, 3, 0|
| 0, 0,−8,−4, 0, 4, 01
| 0, 3,−3,−9,−3, 3, 01
| 0, 4, 0,−4,−8, 0, 0|
| 0, 3, 1,−1,−3,−5, 0|
|5α−35,α−5,α−8,α−9,α−8,α−5,−α|
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α=7を代入すると
=|42, 5, 8, 9, 8, 5, 7|
| 0,−5,−3,−1, 1, 3, 0|
| 0, 0,−8,−4, 0, 4, 01
| 0, 3,−3,−9,−3, 3, 01
| 0, 4, 0,−4,−8, 0, 0|
| 0, 3, 1,−1,−3,−5, 0|
| 0, 2,−1,−2,−1, 2,−7|
=42|−5,−3,−1, 1, 3, 0|
| 0,−8,−4, 0, 4, 01
| 3,−3,−9,−3, 3, 01
| 4, 0,−4,−8, 0, 0|
| 3, 1,−1,−3,−5, 0|
| 2,−1,−2,−1, 2,−7|
=−294|−5,−3,−1, 1, 3|
| 0,−8,−4, 0, 41
| 3,−3,−9,−3, 31
| 4, 0,−4,−8, 0|
| 3, 1,−1,−3,−5|
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