102 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

The ! in any row after the first two is got by multiplying
the g in the same row by the / in the preceding row and sub-
tracting the product from the / in the row before that.

Similarly the m in any row after the first two is got by
multiplying the ¢ in the same row by the m in the preceding
row and subtracting the product from the = in the row
before that.

Other examples:

 

1(23) + 1(— 17) =
2(23) + 3(—17) = —
3(23) + 4(— 17) =
17(23) + 23(— 17) =

 

 

242. Def. If I;_;, my_ and I, my are any pair of successiv
rows of I's and m’s in the tables of § 241, we will let d; stand
for their determinant (1), that is, for ly_ym; — Limj_..

() The determinant of the four numbers a; a;
b1 bs,
written as here in two rows and two columns, is defined as aibs — asgb:.
For this determinant the symbol |a; a;| is used.
bl b2