/’ % '< ? ;■ " gft . 
42 
SOLUTION OF A PROBLEM OF ELIMINATION. 
[391 
which is the required result. It may be remarked that the second and third column 
are obtained from the first by operating on it with A, ^A' J , if A = 28 x + 48 3 + 6S 5 . Or 
say the result is 
(1, A, i A 2 ) 
1235 
3451 
5613 
In like manner for the system 
if the columns are 
then the result is 
a? 
xHj, 
cPif, xhf, xy\ 
f 
a 
b , 
c , d , e 
f 
a' 
b' , 
c' , d' , e 
f 
a", 
b", 
c" , d" , e" , 
r 
a'" 
b'", 
c"', d'", eT , 
r 
a b, 
a' V, a" b", 
a'" b"\ 
b c, 
V c', b"c", 
b'" c'", 
c d, 
c’ d\ c" d", 
c” d'", 
d e, 
d! e, d n e", 
d"' 
e f> 
e'f', e"f"> 
1, 2, 
3, 4, 5, 6, 
7, 8; 
(1, A, * A«) 
12357 
34571 
56713 
78135 
= 0, 
where 
A = 28 1 + 48 3 + 68 5 + 8\ 7 .