RESULTANTS. 1438 
and let its inverse 7 be written, 
A 
— a2= Ain, + Ay + Ast, 
p 
A 
— y2=Bix,+ Boyi+ Bazi, 
FE ? 
A 
— 42> Cx, + Cry, + C32, . 
P 
(12) 
Forming the resultant by the method of Art. 175, we have, 
xu 
Aj 
. A2 — 
Ti AP%= 74, 
|As 
F |4. By G| 
Since | 4: Bo GC 
A; Bs 
Cs 
Ye 0 ne 0 
By Gi Ai 2, || At Bi (Gr By) 
Bo Co As|? = C= Az Bo C2 Be}? 
Bs C3 As As Bs Cs Bs| 
| 2 Yh Vz 0 | 
pp, — ||\4n ten (En Gu) 
+ me = | Ao Bo Co Co|* ( 14) 
As Bs Cs Cs | 
= A’, the equations of T, reduce to x,=4,, 
Yo = Y, %. = 2%; thus T, is the identical collineation. 
d. 
THEOREM 
The resultant of any collineation 7 and its inverse 
is the identical collineation. 
178. Resultant in the Normal Form. Let Tand T, be two 
collineations in homogeneous normal forms, 
A: 
(1X2 
Pv, = 
x Yy z 0 )2 8 2 z 
ABs 1G) A Pee PAl BiG. B 
AB © KA) PYr>= |r Bee xB |» 
Al Bl Cc" kA! | A” Bl Cc" kB! | 
% yY 2 0 
AEB: TC: C | 
Pia WAUea RCT CK: (15) 
Al Bl Cc" k/C” 
a yl Za 0 | Yl Az 0 | 
A Bm GM Ai | 1 _ |40 Bh Gi By | 
Ay! BY Gi! knAy! |? 0242) ay By Gi! ln By |? 
Ai” By!’ Cy! ky! Ay!’ | | Aa” By’ Cy” ky! By!’ | 
v1 Yi aA 0 | 
os Aj By Cy Ci / 
01%. = Al 7280 Gl TeyGNI||° (15 ) 
| Ai!” Ba! Ci!’ ky’ Cy") 
