# Changes to Determinants

• Nov 5th 2008, 02:12 PM
Hellreaver
Changes to Determinants
I need to find the determinant given that A is a 4X4 matrix for which det(A)= -2.

Where det(2A^T)

I would guess I need to find the transpose of the matrix A's determinant, which is the same as det(A), and then multiply the resultant by 2, but I don't think that is right... What needs to be done here?

Note: using various examples, I found that the determinant of A after the Matrix A has been multiplied by 2 results in the determinant being multiplied by 16, which makes sense because, being 4X4, would make it 2^4... Would -32 be the correct answer for this question?
• Nov 5th 2008, 05:29 PM
ThePerfectHacker
Quote:

Originally Posted by Hellreaver
I need to find the determinant given that A is a 4X4 matrix for which det(A)= -2.

Where det(2A^T)

\$\displaystyle \det (2A^T) = 2^4 \det (A^T) = 2^4 \det (A) = -2^5\$
• Nov 5th 2008, 08:08 PM
Hellreaver
Quote:

Originally Posted by ThePerfectHacker
\$\displaystyle \det (2A^T) = 2^4 \det (A^T) = 2^4 \det (A) = -2^5\$

Its 2^4 because the matrix is 4X4, I'm assuming?
• Nov 5th 2008, 08:41 PM
ThePerfectHacker
Quote:

Originally Posted by Hellreaver
Its 2^4 because the matrix is 4X4, I'm assuming?

Yes (Clapping). Exactly!
• Nov 5th 2008, 08:43 PM
Hellreaver
About time I didn't fail at something miserably. Thanks again...