MATHEMATICAL APPENDICES. 



203 



Multiplying equations (14) by k, and changing signs throughout, 

 we get 



TH kri)ii + pM^ + pMi 3 i 3 4- . . + pMi n i n = ke 



- kr 3 )i 3 -f . . . -f pM^in = ke }. (2) 



therefore 



. _^v; 



where 



= ke, pMw, pMi 3 , pMi 



ke, pM 3 %, pMw kr 3 , . . . pM 3n . . . (3) 



ke, pM n <2, pM^, . . . pM nn kr n 

 and 



Ti 3 , . . . pM ln 



... pM* 



r, l3 , . . . pM )m - Ar w 

 Xow 



1, 



where 



1, 



and A', is A' with the sth row and column erased 



A',, is A' with both sth and th rows and columns erased, 

 and so on 



