Find Determinants using montante (bareiss algorithm) ...
`[[1,1,1],[-1,-3,-3],[2,4,4]]`

Solution:

`A`

=

`1` `1` `1` `-1` `-3` `-3` `2` `4` `4`

Step-0: Previous Pivot `=1`

Step-1: Pivot `=A_(1,1)=1`, Previous Pivot `=1`

`A_(i,j)=(A_(1,1) * A_(i,j) - A_(i,1) * A_(1,j))/(1)`, where `i>1` and `j>1`

`A_(2,2)=(1 * -3 - -1 * 1)/(1)=-2`

`A_(2,3)=(1 * -3 - -1 * 1)/(1)=-2`

`A_(3,2)=(1 * 4 - 2 * 1)/(1)=2`

`A_(3,3)=(1 * 4 - 2 * 1)/(1)=2`

So matrix becomes

`A`

=

`1` `1` `1` `-1` `-2` `-2` `2` `2` `2`

Step-2: Pivot `=A_(2,2)=-2`, Previous Pivot `=1`

`A_(i,j)=(A_(2,2) * A_(i,j) - A_(i,2) * A_(2,j))/(1)`, where `i>2` and `j>2`

`A_(3,3)=(-2 * 2 - 2 * -2)/(1)=0`

So matrix becomes

`A`

=

`1` `1` `1` `-1` `-2` `-2` `2` `2` `0`

Determinant will be `A_(3,3)` multiplied by the scaling factor 1

`:.` Determinant `=0`

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