1917-18.] Determinants of a 4— by—8 Array. 
225 
18 . For a last example we may give the set which concerns the result of 
diminishing the sum of the non-diagonal elements of a row of | b 13 j by the 
sum of the non-diagonal elements of the corresponding column of | c 13 \ . 
This is 
^12 ~ C 21 + ^13 ~ C 31 ~ ~ ^11 ^ ^22 ’ 
^21 ~ C 12 + ^23 ” C 32 = — Al + ^33 J 
^31 — C 13 ■** ^32 ~ C 23 = — ^11 ^44 * 
An alternative for the set is got by changing the elements in each case into 
the conjugate elements; and from either set by addition there is obtained 
the similarly obtained result of the preceding paragraph. 
Rondebosch, S.A., 
4th April 1918. 
( Issued separately January 31, 1919.) 
VOL. XXXVIII. 
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