Maths help?

[2xMachina]

Does anyone knows how to get |A| (determinant of A), when the only thing given is the "adj A" (adjoint of A)

If it helps, it's a little special, with zeroes on some places.

adj A is:


|a b 0 0|
|c d 0 0|
|0 0 e 0|
|0 0 0 f|

[mucat]

Does anyone knows how to get |A| (determinant of A), when the only thing given is the "adj A" (adjoint of A)

If it helps, it's a little special, with zeroes on some places.

adj A is:


|a b 0 0|
|c d 0 0|
|0 0 e 0|
|0 0 0 f|


Dude, you know what an adjoint is, right? If they gave you the adjoint of A, they've essentially given you A itself.

Two ways you can do it:
(1) Just take the adjoint again to get back to the original matrix A (which in this case, just means swapping b and c, and taking the complex conjugates of all the elements.) Then take the determinant as you always would.

(2) Don't bother to reconstruct A; the determinant of adj(A) will be the complex conjugate of the determinant of A. So just take the determinant of the matrix they gave you, then take the complex conjugate of that number, and you're done.

[2xMachina]

Thanks.

I missed that relation.

It seems to want (2), considering it asked for |adj A| in the first part, and then A later.

Say, I got the determinant to be 40. The complex conjugate is still 40 right? (Since there's no imaginary number)

[mucat]

Exactly.

Just think of it as 40 + 0i

[2xMachina]

Thanks.

/me comments that the internet is a good place to learn.