Oznaczenia z informatyki a -= b onzacza, ze a zamienia sie na a-b

|1 1 1 1|
|1 2 2 2|
|1 2 3 3|
|1 2 3 4|
IV -= III, III -= II, II -= I 
=
|1 1 1 1|
|0 1 1 1|
|0 0 0 1|
|0 0 0 1|
= 1
----------
|1 1 1  1 |
|1 2 3  4 |
|1 3 6  10|
|1 4 10 20|
IV -= III, III -= II, II -= I 
=
|1 1 1  1|
|0 1 2  3|
|0 1 3  6|
|0 1 4 10|
IV -= III, III -= II
=
|1 1 1 1|
|0 1 2 3|
|0 0 1 3|
|0 0 1 4|
=
|1 1 1 1|
|0 1 2 3|
|0 0 1 3|
|0 0 0 1|
= 1
-------------
|3 6 0 5|
|0 7 0 2|
|1 8 4 9|
|0 1 0 0|
zamiana wierszy II i III
= -
|3 6 0 5|
|1 8 4 9|
|0 7 0 2|
|0 1 0 0|
zamiana wierszy I i II
=
|1 8 4 9|
|3 6 0 5|
|0 7 0 2|
|0 1 0 0|
zamiana kolumn I i III
= -
|4 8 1 9|
|0 6 3 5|
|0 7 0 2|
|0 1 0 0|
zamiana kolumn II i III
=
|4 1 8 9|
|0 3 6 5|
|0 0 7 2|
|0 0 1 0|
zamiana kolumn III i IV
= -
|4 1 9 8|
|0 3 5 6|
|0 0 2 7|
|0 0 0 1| = -24
---------------
|x 1 1 1|
|1 x 1 1|
|1 1 x 1|
|1 1 1 x|
=
|x    1   1   1 |
|1    x   1   1 |
|1    1   x   1 |
|x+3 x+3 x+3 x+3|
= (x+3)
|x 1 1 1|
|1 x 1 1|
|1 1 x 1|
|1 1 1 1|
=
= (x+3)
|x-1  0 0  0|
|0  x-1 0  0|
|0   0 x-1 0|
|1   1  1  1|
= (x+3)(x-1)^3
-----------------
|101 3 2|
|102 5 1|
|103 4 7|
=
100*
|1 3 2|
|1 5 1|
|1 4 7|
+
|1 3 2|
|2 5 1|
|3 4 7|
= ...
100*(35+8+3-10-4-21) + (35+9+16-30-42-4)=100*11-16=1084