Question 1207027
.



According to the cofactoring theorem for matrices and determinants,
you should take common factor  -3  (= negative 3)  with matrix  F
and multiply it by  |M| = 5,  so the final determinant for matrix  F  is


                |F| = (-3)*5 = -15.



With matrix  G,  your understanding is correct and the final answer is correct, too.



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To learn on how cofactoring works for 3x3  determinants,  see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Determinant-of-a-3x3-matrix.lesson>Determinant of a 3x3 matrix</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Co-factoring-a-3x3-determinant.lesson>Co-factoring the determinant of a 3x3 matrix</A> 

in this site. &nbsp;&nbsp;It is very similar for matrices of higher dimensions.