1. Find Determinants using montante (bareiss algorithm) ...
`[[8,-6,2],[-6,7,-4],[2,-4,3]]`

Solution:

`A`

=

`8` `-6` `2` `-6` `7` `-4` `2` `-4` `3`

Step-0: Previous Pivot `=1`

Step-1: Pivot `=A_(1,1)=8`, 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)=(8 * 7 - -6 * -6)/(1)=20`

`A_(2,3)=(8 * -4 - -6 * 2)/(1)=-20`

`A_(3,2)=(8 * -4 - 2 * -6)/(1)=-20`

`A_(3,3)=(8 * 3 - 2 * 2)/(1)=20`

So matrix becomes

`A`

=

`8` `-6` `2` `-6` `20` `-20` `2` `-20` `20`

Step-2: Pivot `=A_(2,2)=20`, Previous Pivot `=8`

`A_(i,j)=(A_(2,2) * A_(i,j) - A_(i,2) * A_(2,j))/(8)`, where `i>2` and `j>2`

`A_(3,3)=(20 * 20 - -20 * -20)/(8)=0`

So matrix becomes

`A`

=

`8` `-6` `2` `-6` `20` `-20` `2` `-20` `0`

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

`:.` Determinant `=0`

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