Sylvester's and other Unisignants. 
195 
and then into 
1 1 
1 6' 
^4 ^5 
C6 ^4 + '^356 + ^4 
are not difficult to see. They suffice to show that the sum of the signed 
primary minors of 
M(a ; h^jjjjjb^ ; c^c^cx^c^Ce ; d^d^d^d^) 
is the same as the sum of the signed lyrimary minors of 
M(0; 0000; c,c^cx,c^Ce\ b, + d,, b, + d„ b, + d^, b, + d^) (XYII.) 
The next operations are 
row. - roWa, row^ - roWa, row^ - roWa 
C0I3 - C0I2, C0I4-C0I2, C0I5 — C0I2, 
which will be found to lead to 
^12 + C2345 + t?i2 b, + c^^ + d, b, + c^^^ + d, 
j b, + c^^ + d, ^i3 + c,346 + ^^i3 b, + c,e + d, 
I b, + c^^ + d, b,i-c,e + d, b,^ + c,^^e + d,^ 
i.e., to 
b, + d, + c. 
61 + + C25 + C34 + + ^1+^1 + ^34 
&i + ^i + 6'34 b, + d, + c^e + c.^ + b. + d. K + ^h + c^^ 
b^ + d, + K+J^ + b^ + d, + + c^^ + b^ + d^ !; 
so that the sum of the signed primary minors of is equal to 
M(^i + f?i ; + C6, + C5, C3 + C4 ; + d^, b. + f/3, b^ + c?^). 
By the usual method the number of terms in the final development of 
the bordered M„ is ascertained to be 
2 
in— 2) (n— I) 
(XVIII.) 
