.106 
Proceedings of Royal Society of Edinburgh. [: 
let us first perform the operations* 
colj - col 3 + col 5 - col 7 , 
col 2 - col 4 + col 6 - col 8 , 
col 3 - col 5 + col 7 , 
col 4 - col 6 + col 8 , 
col 5 - col 7 , 
colg — colg ,, 
with the result 
X 
7 
-7 
X 
6 
— X 
- 7 
X 
5 
7 
- X 
-7 
X 
4 
X 
7 
- X 
-7 
X 
3 
-7 
X 
7 
- X 
-7 
X 
2 
- X 
- 7 
X 
7 
- X 
-7 
X 
7 
- X 
-7 
X 
7 
- X 
- 7 
1 
x • 
Next let us increase the 8th row by the 6th, the 7th by the 5th, 
and so on, and we obtain 
x 7 | 
- 7 x 6 . . . . 
x 5 . . . [ 
- 1 x 4 . . I 
. . , -2 x 3 . . 
.-3x2. 
- 4 x 1 
-5 .;x I 
* These are equivalent to multiplication row-wiso by unity in the form 
