12]
by putting
Hence,
ON THE THEORY OF DETERMINANTS.
A = a (rA+r'A'+...) + b (rB + k'B'+ ...) + ....
B = a (sA +s'A'+ ...)+ b (sB + s'B'+ ...)+ ...,
A' = a'(rA + b?A'+ ...) + b' (rB+r , 5 / +...) + ...,
B' = a' (sA + s'A' + ...)+ b' (s B +s'B' + ...) + ...,
KFU =
A, B,...
R, S,...
A,
B,...
A', B',
r', s',
A',
or observing the equation (14), and writing
A, B,..
a', b',
this becomes
Hence likewise
Consider next the equation
'XFU = —
: j
KFU = JF. (.KU) n ~ 1
K1U=JC .{KU) n ~ l
A^ + B?; + ..., A
A'Z + B'y+..., A'
R# + R V + ..., SX + S V + ...,
B
B'
1,
1,
t
v , •••
A, B,...
R, S, ...
X, A,
B,
A', B',
r', s',
x\ A',
B',