11 ao 



ill whirh 7^- i« obtained by omitting the row ciki in the nuitrix M. 

 So we find 



in which tlie summation must be extended over all determinants of 

 the {(y—lf' order, resp. of the matrices Mj and Mj,, and this in 

 snch a way that the determinants Dj and D], in the products are 

 built up from the same columns of M. 



The coefficients hji,{j:=zl,2,...Q; yl—1, 2, ...9) are finally found 

 from 



so that 



Lbji, . A'-^-i :ed^ = i--iy+j {-i)r+k A^-r :s:ijjDi,, 





and in jiarticular 



Q'|=l,2, ..,), 



""JJ 





0=1,2, ...p) 



The determinant of the coefficients l)jk{j, k ^1,2, 

 621 , 622 , . . . 62. , , 



hi^ I 



or, if we write 



, ,...0 , />,+!,,+!, 



, ,...0 , , i,+.>,,+'i 



Ö , d , . . , Ó 



ell 1 ^12 , • . . 61 £ 



0-21 , />22 i • • • ^2i 

 ^Pl 5 ^p2 1 ■ ■ ■ b^c 







0) runs 



.. 

 . . 



. . (] 



..0 

 .. 



= E 



E is the determinant of the quadratic expression // in :c^, :v^, ... x^ 

 As the determinant quadratic expression in v„v^,...v, has the 

 value 1, we have 



*i* I = A^ ' 



hence 



