370 
[59 
59. 
ON THE THEORY OF ELIMINATION. 
[From the Cambridge and Dublin Mathematical Journal, vol. ill. (1848), pp. 116—120.] 
Suppose the variables Xj, X 2 ..., g in number, are connected by the h linear 
equations 
Oj —a l X 1 + a 2 X 2 ... = 0, 
® 2 = ¡3 1 X 1 + /3 2 X 2 ... = 0, 
these equations not being all independent, but connected by the k linear equations 
<t>x = a/ + ... = 0, 
^ = /m+A/e 2 +--. = o, 
these last equations not being independent, but connected by the l linear equations 
+ a./' d? 2 + ... = (), 
= /3x"<E>x + &"<I> 2 + .. . = 0, 
and so on for any number of systems of equations. 
Suppose also that g — h + k —1+... = 0; in which case the number of quantities 
X x , X 2 ,... will be equal to the number of really independent equations connecting 
them, and we may obtain by the elimination of these quantities a result V = 0.