1878.] 



of coordinates. 



179 



[a, h, gj^x, y, z\^, r), i;), = { a, h, g \^, rj, \;\x, y, z), 



h, b, f 



g, /» c 



h, h, f 



9^ /' c 



is also written 



{a, h, c, f, g, lij^x, y, zj^, v, ?), or {a, ... J^, v, ^l-^, y, ^), 

 and in particular, if 



then 



( a, h, g \x, y, zf is written* [a, h, c, f, g, h\x, y, zf. 

 K h, f 



g, /, c 



Two matrices are compounded together according to the law 



(a,^',a"), {I3,l3',n, (7,7.7% 



{a , b , c ][a,/3,7 ) = {a , b , c) 



a , b' , c 

 a", b", c" 



'a' I 



a , P , 7 



0. , P , y 



(a , b' , c) 

 [a , b , c ) 



viz., in the compound matrix, the top-line is 



{a, b, c^oi, a, a"), (a, b, c$^^, ^', (3"), {a, b, c]^7', 7", 7"). 



and the other two lines are the like functions with (a, b', c) and 

 {a", b", c") respectively in the place of {a, b, c). 



The inverse matrix is the matrix the terms of which are the 

 minors of the determinant formed out of the original matrix, each 

 minor divided by this determinant, viz., 



( a , /S , 7 )"' = - ( ^'y" - /3'V, /S"7 - /37", ^7 - ^7 ) > 



a , /3 , 7 

 a", ^", 7" 



7'a" —y"a , 7 a — 7X , 7a —7a 

 7"a -ya", a"/3-a^", a^' - a'^ 



where v is the determinant 



a , /3 , 7 



' ID' ' 



a , P , 7 



a", ^", 7" 



