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復(fù)旦大學(xué)謝啟鴻高等代數(shù)每周一題[2021A01]參考解答

2021-10-06 17:52 作者:CharlesMa0606 0人讀過 | 我要投稿

本文是本人給出的2021年復(fù)旦大學(xué)謝啟鴻高等代數(shù)的每周一題[問題2021A01]的解答

題目來自于復(fù)旦大學(xué)謝啟鴻教授在他的博客提供的每周一題練習(xí)

（鏈接：https://www.cnblogs.com/torsor/p/15329047.html）

[問題2021A01]求下列階行列式的值：

$%5Cleft%7CA%5Cright%7C%3D%5Cleft%7C%5Cbegin%7Bmatrix%7D1%26a%26a%5E2%26%5Ccdots%26a%5E%7Bn-1%7D%5C%5Ca%261%26a%26%5Ccdots%26a%5E%7Bn-2%7D%5C%5Ca%5E2%26a%261%26%5Ccdots%26a%5E%7Bn-3%7D%5C%5C%5Cvdots%26%5Cvdots%26%5Cvdots%26%5C%20%26%5Cvdots%5C%5Ca%5E%7Bn-1%7D%26a%5E%7Bn-2%7D%26a%5E%7Bn-3%7D%26%5Ccdots%261%5C%5C%5Cend%7Bmatrix%7D%5Cright%7C.%0A$

解?? $%E5%B0%86%E7%AC%ACi%E5%88%97%E4%B9%98%E4%BB%A5-a%E5%8A%A0%E5%88%B0%E7%AC%ACi-1%E5%88%97%E4%B8%8A%5Cleft(i%3D2%2C3%2C%5Ccdots%2Cn%5Cright)%EF%BC%8C%E6%9C%89%EF%BC%9A$

$%5Cleft%7CA%5Cright%7C%3D%5Cleft%7C%5Cbegin%7Bmatrix%7D1-a%5E2%26a%5Cleft(1-a%5E2%5Cright)%26a%5E2%5Cleft(1-a%5E2%5Cright)%26%5Ccdots%26a%5E%7Bn-1%7D%5C%5C0%261-a%5E2%26a%5Cleft(1-a%5E2%5Cright)%26%5Ccdots%26a%5E%7Bn-2%7D%5C%5C0%260%261-a%5E2%26%5Ccdots%26a%5E%7Bn-3%7D%5C%5C%5Cvdots%26%5Cvdots%26%5Cvdots%26%5C%20%26%5Cvdots%5C%5C0%260%260%26%5Ccdots%261%5C%5C%5Cend%7Bmatrix%7D%5Cright%7C.%0A$