數學 matrix

👨🏻‍🏫 學術台數學

2012-04-05 8:17 pm

Show that if A is a 3 by 3 matrix such that A ^T= -A, then det A =0

更新1:

不好意思,第2步是怎樣來的?可否指教我?thx

回答 (2)

2012-04-06 2:03 am

✔ 最佳答案

DET (A^T) = DET(-A)
DET A = (-1)^3(DETA)
DET A = -DET A
2DET A = 0
DET A =0

參考: ME

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知識就是力量

2012-04-06 6:48 am

For any n x n matrix, det (kA) = k^n det A

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