81 
1906-7.] Dr Muir on Minors of a Product-Determinant. 
and the aggregate of terms in b 3 to be 
A, h 2 A s 
m 2 m 3 
/1 /* ft 
n 2 ^ 3 
r 2 ^3 
The minor in full is therefore 
^2 ^3 
9i 9 2 9 3 
m 2 m 3 
n 2 n 3 
/l /2 /3 
• 
m 2 m 3 
+ | &1 c 3 1 . 
f\f 2 f% 
m 2 m 3 
+ 1 ^2 C 3 1 * 
9i 92 9s 
• m 2 m 3 
9i 92 9s 
w 3 
h\ h 2 h 3 
72 2 W 3 
h l h 2 h 3 
n 2 n z 
r 2 r 3 
r 2 r 3 
r 2 r 3 
i.e. A 3 (H 3 R 1 + H 2 N x + HjMj) 
+ A 2 (G 8 R 1 +G 2 N 1 + G 1 M 1 ) 
+ A 1 (F 3 R 1 + F 2 N 1 + F 1 M 1 ); 
so that, formulating as before, we have the result — In the determinant 
which is the 'product of \ a x b 2 c 3 | , | f x g 2 h 3 | , | m x n 2 r 3 | the co factor of 
^2 ^3 Aj A 0 "A3 
fi 
gl 
h i 
IS 
*1 
Gi 
H, 
M, 
U 
§2 
n i 
f 2 
G 2 
h 2 
^3 
§3 
hs 
T 1 
f 3 
g 3 
h 3 
Ei 
3. Just as the minor in § 1 is the result of the multiplication 
b i h h 
fi fi 
C 1 C 2 C 3 
9i ffs 
h 2 h 3 
so the minor in § 2 is the result of the multiplication 
b 1 b 2 b 3 
fi A fi 
m 2 m s 
C l C 2 C 3 
9i 92 9s 
n 2 n z 
h Y h 2 h 3 
r 2 r 3 
and, the former being used as a symbol for the minor to which it gives rise, 
the latter may with convenience be similarly employed. Further, we 
may utilise the first result in establishing the second : for, the first being 
the second 
h\ b 2 b 3 
/l/ 2 
C ] C 2 C 3 
9i 92 
\ h 2 
VOL. XXVII. 
A 3 H x + A 2 Gj + AjFj 
b 2 b 3 b x b 2 b 3 & 1 b 2 b 3 
fi 9\ \ f 2 92 h-2 f 3 9 2 , ^3 
Ci Co Co Ci Co Co Ci Co Co 
f 1 9\ hi / 2 92 h <2 f 3 9s h 3 
v 2 
h\ ^2 ^3 
C 1 C 2 C 3 
I fifz 
\9i 9s 
h\ h 3 
m 2 
m s 
n 2 
n 3 
V 2 
r 3 
’2 r 3 
1 + 
[61 b. 
\ Ci c. 
uu 
92 9s | 
K h% 
6 
n 2 r 3 I 
