can be written in terms of the determinants of
sub-matrices
(4)
In general, each element of the top row of the matrix is
multiplied by the determinant of the sub-matrix obtained by removing
the row and column containing that element. The results are
then added together with alternating sign, starting with a positive
term. Figure 1 shows the top-row elements and
the associated sub-matrices and signs for the , , and cases.
Figure 1:
A visual guide to computing the determinants of , , and matrices.