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hgj

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- Thread starter hgj
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- #1

hgj

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- #2

JoAuSc

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Well, a determinant of a matrix is the sum of the products of its diagonals minus the products of its antidiagonals. How do these products change under a transpose?hgj said:

- #3

amcavoy

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[tex]\det{A}=\sum_{i=1}^{m}\left(-1\right)^{i+j}a_{ij}\det{A_{ij}}[/tex]

Do you see what happens when you try to prove det(A^{T})=det(A) for 2x2 or 3x3 matrices? Use the definition.

Edit: To the above poster: Doesn't that definition only work for 3x3 matrices?

Do you see what happens when you try to prove det(A

Edit: To the above poster: Doesn't that definition only work for 3x3 matrices?

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- #4

Hurkyl

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apmcavoy: I don't believe that formula helps, at least not in a straightforward manner.

hgj: what are you using as the

- #5

hgj

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detA = a11det(A11) - a21*det(A21) + ... + (-1)^(n+1)*an1*det(An1)

(sorry, I don't know how to make things subscripts on this, so the 11, 21,...,n1 are supposed to be subscripts)

That's the definition we're using for a determinant.

- #6

amcavoy

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hgj said:

detA = a11det(A11) - a21*det(A21) + ... + (-1)^(n+1)*an1*det(An1)

(sorry, I don't know how to make things subscripts on this, so the 11, 21,...,n1 are supposed to be subscripts)

That's the definition we're using for a determinant.

Ok, that's the same thing I posted above. I suppose you could write it out like you did for both A and A

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