This scheme will be formed of six diagonals with three different elements of
determinants. The elements products in three diagonals in left side will get the “+”
sign, in the other hand the elements products in three other different diagonals in right
side will get “-“sign. This will produce three terms with “+”sign and three other terms
with “-“sign, which in fact presents the definition formula to compute the
determinants of third order.
This new method consists of two other schemes, which will be formed in the same
way like the preliminary scheme (Scheme 5) but these two other different schemes
manipulate with elements in other rows and columns from the Scheme 5.
The other forms of this method are shown in the following schemes (Scheme 6,
Scheme 7)
The results acquired by using the “NEW METHOD” are entirely equal with the
results acquired by the other known methods until now (definition of determinants,
Sarrus’s Rule, Triangle’s rule, expansion by the elements of whatever row or column,
Chio’s condensation, Dodgson’s condensation). In base of this, we can conclude that
this new method to compute the determinants of third order is true and can be used
only for the third order determinant. Also we must pronounce, that this new method
has relates and sameness with also new methods to compute determinants of higher
order than that of the third order (n>3).