276 Transactions of the Boyal Society of South Africa. 
By performing on this last the operations 
roWj - \~ 
roWa - X~ 
row. 
row^ 
row. 
- row6[- 
- row. ) , 
col^ + X-^ C0I2] 
C0I5 + C0I2 [ 
cole + colj 
there is obtained 
-a^X^ 
a, 
3-^X3 
— ft A3 
a^X — aeX^ a^ 
a^ — a^X — a.X 
a^X — a.X^ ao~-a^X^ 
a^X — a^X^ a^^ — a^X^ 
a^X — a^X^ a^ — a^X^ 
-a^X^ 
-^5X3 
D-«6X3 
- «.5X3 
-aeX^ 
which, when we have multiphed the 3rd row and divided the 3rd column 
by X and have reversed the order of the last fom' columns, and thereafter 
of the last four rows, becomes 
(^0-^6^3) 
-aeX^ 
-aeX^ 
-a,X3 
«2 
a, 
3-^5X3 
-^5X3 
— aX^ 
a. 
~aeX' 
— a^X^ 
-a,X' 
-a.X 
a^X-aeX^ 
a^X — a^X^ 
a^X — a^X^ 
a^X — a.X^ 
«o — <^2X 
as desired. 
ori 
ginal 
paper 
1 
2 
37 
46 
37 
0 
17 
26 
35 
26 
74 
06 
15 
24 
15 
64 
53 
04 
13 
04 
13-X 
04 
64 
24-X 
15 
06 
74 
35X 
26 
17 
0 
46-X 
37 
2 
1 
we perform the operations 
roWi — X~' roWy 
row2 — X~' rowe 
roWj — X~' row5 
row. 
C0I3 + C0I2 \ 
C0I7 + C0I3 + X~' coll 
cole + X~' C0I2 
C0I5 + X~' C0I3 / 
