线性代数矩阵,第三题,后面两个怎么证明

2025-01-01 08:54:26
推荐回答(1个)
回答1:

(1) n = 2 时,|A1| = - |A| , |A2| = - |A^T| = - |A| ;
n = 3 时,|A1| = - |A| , |A2| = - |A^T| = - |A| ;
n = 4 时,|A1| = (-1)^2 |A| = |A|, |A2| = (-1)^2 |A^T| = |A| ;
n = 5 时,|A1| = (-1)^2 |A| = |A|, |A2| = (-1)^2 |A^T| = |A| ;
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|A1| = |A2| = (-1)^[(1/2)n(n-1)] |A| .
(2) A3 相当于 A 变成 A2,再按 A2 方法变化,故
|A3| = (-1)^[(1/2)n(n-1)] (-1)^[(1/2)n(n-1)] |A| = |A|