WebOrange Blossom Hills allows you to enjoy life at your own pace…at any age. Whether it is shopping and dining by day or the nightlife The Villages has to offer, this is the community for you. You can experience the true hometown feel by visiting any of the three old … Web6. Take A = I n = B. Then det ( A + B) = det ( 2 I n) = 2 n det ( I n) = 2 n and det ( A) + det ( B) = 1 + 1 = 2 so for n > 1, your equality does not hold at least for these matrix. And for n = 1, since the determinant is the only element of the matrix, we do have your equality. So [ ∀ A, B ∈ M n ( R), det ( A + B) = det ( A) + det ( B)] n 1.
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linear algebra - Does $\det(A + B) = \det(A) + \det(B)$ hold ...
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