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

DETERMINANTS IN GENERAL (MAJO, 1854)

85

of Bezout (1764), and gives one or two very elementary properties
of it. The remaining ten pages are occupied with simultaneous
linear equations, and are notable as containing (~~ 15-19) a clear
exposition of Bezout's peculiar rule-of-thumb process of 1779.
Herein lies the value of the paper, Majo being not only the first
since Hindenburg to recall attention to a neglected process of
real practical value, but also the first to give (~ 16) a reason for
its validity.
CAYLEY, A. (1854, May).
[Remarques sur la notation des fonctions algebriques. Crelle's
Journal, 1. pp. 282-285; or Collected Math. Papers, ii.
pp. 185-188.]
The notation referred to is that of matrices, and is exemplified by
( 1 Ct2 3 )
(a1 /2.3
7Y 72 73,
a matrix being defined as a system of quantities arranged in
the form of a square, but otherwise quite independent. With
its help the set of equations
= a1x+a2y+ a3Z
r = blX —b2y +b3z
C1= Cx + c2y 3
may, he says, be written in the form, ^ < a= ( a 2 a3, y, Y ),
bl b2 b3
C1 C2 C3
and consequently the solution of the set in the form, y, z = ( A B1 C1 V i, A e).
A A A
A2 B2 C2
A A A
A_ B3 C3
A A A