It is often stated that Cramer’s rule which gives solutions
of linear systems as quotients of determinants is generally
impractical [9], [11], quickly getting long and tedious as the
number of the unknowns of the system increases. This is so
because as the number of the unknowns increases, the num-
ber of determinants involved and their orders increase in equal
proportion, causing one to give up hope of ever solving such a
system. One way of curtailing the amount of labour, time and
computation to a reasonable level when using Cramer’s rule
is to adopt a brief method of computing large determinants
[9] such as Dodgson’s condensation which we have already
discussed in Section II. Here we shall never refer to this ap-
proach, but we shall discuss a new, simpler and better one
which is derived from Cramer’s rule but employs Dodgson’s
condensation in its calculations