Matrix

👨🏻‍🏫 學術台數學

[匿名]

2011-10-20 1:44 am

A is a 3 x 3 square matrix. If A + A transpose = 0, show that det A = 0.

回答 (1)

Prof. Physics

2011-10-20 2:16 am

✔ 最佳答案

I'll write A^T as A transpose

As:

A + A^T = 0

A = -A^T

det(A) = det(-A^T)

det(A) = - det(A^T)

But we know det(A^T) = det(A)

So, det(A) = - det(A)

2det(A) = 0

So, det(A) = 0

參考: Prof. Physics

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