The theory of determinants in the historical order of development, by Sir Thomas Muir.

LINEAR EQUATIONS (VENTE'JOLS, 1877)

93

set of linear homogeneous equations it takes with D'Ovidio the
following form: If
(XV~p P (1), X0?) )
be r independent solutions of the set q/ equations
(1) (1) ___
a X1 -i.+-a,,, a X
then the primary minors of
(1) (1) i
X(r) Q(r)
are proportional to those of
a(1) (1)
1 ~~~~~~~~~it
a1.,2 a a62.
the ratio
(- W X 3Cd) r?) I: I a(')
a a 0.
being constant if a,..., b, e,..., d be a permutation of 1, 2,...,
and have w inverted-pairs.
Biehier opens his thesis (pp. 5-10) with the solution of n linear
equations in n unknowns; he does not, however, give anything
really fresh.