258 



M (r, 2 , r, 3 ) = 



PROFESSOR K. PEARSON AND MR. L. N. G. FILON 



R + R,,, r 12 R 12 , R 13> 



r 12 R ]2 , R + R 22 , 0, R 23 



R , r i 



Add the third column, multiplied by r, 3 to, and subtract the fourth multiplied by 

 .,;, from, the second, and then subtract the first 



n v __ __ _ 

 <rirl<rR 5 



R + R n , - 2Tl n , 



igBja + ^'is 



2l\,o 3 , 



0, 



R,, 3 , R, : , 



Divide out the 2 in the second column, add it to the first, and subtract the third 

 column multiplied by r 13 



4jj5 j> ?-R. R R I 



M (?>, r 13 ) = -- , -,. ! 



: R - ?', 3 R, :i , R, 2 , 0, R 23 



?- 12 R; i:! , 0, R 2:i , R, 3 



rv> : j , ?Vj . ?*| 2 , 



Add r.,;, times the last row to the first 



M (r,,, ?) = 



i> o .) -r > - 



crjcrjcrjli-' 



1 33> 



R - 



&aa> R22> 0, R 2; 



r ^R 0, Ro. R , 



- "R r - r 1 



-"23? ' 23 ' 12i 



Subtract r 23 times the first row from the last, and remember that R 23 ?' 23 R 33 =r, 2 R 



1 s, 



R ?* 2 3R23 R22, 0, R 23 



*Riii o R23) RIS 



r, 2 R 13 , 0, R 12 , R u 



Multiply the first row by R 22 and add it to the second ; the determinant reduces 

 to the third order, 



M (>',!>, r a ) = 



R ?' 23 R 



2323 



13 R 12 



R23J 



R, 2 , 



