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Code is changed on 22.07.2025, Now it also works for Complex Number.
For wrong or incomplete solution, please submit the feedback form.
So, I will try my best to improve it soon.
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Solution
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Solution provided by AtoZmath.com
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Determinants using montante (bareiss algorithm) calculator
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 1. `[[8,-6,2],[-6,7,-4],[2,-4,3]]`
2. `[[6,-2,2],[-2,3,-1],[2,-1,3]]`
3. `[[3,2,4],[2,0,2],[4,2,3]]`
4. `[[1,1,1],[-1,-3,-3],[2,4,4]]`
5. `[[2,3],[4,10]]`
6. `[[5,1],[4,2]]`
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Example1. Find Determinants using montante (bareiss algorithm) ...
`[[1,2,3],[0,1,0],[2,3,1]]`Solution:| `A` | = | | `1` | `2` | `3` | | | `0` | `1` | `0` | | | `2` | `3` | `1` | |
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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 * 1 - 0 * 2)/(1)=1` `A_(2,3)=(1 * 0 - 0 * 3)/(1)=0` `A_(3,2)=(1 * 3 - 2 * 2)/(1)=-1` `A_(3,3)=(1 * 1 - 2 * 3)/(1)=-5` So matrix becomes | `A` | = | | `1` | `2` | `3` | | | `0` | `1` | `0` | | | `2` | `-1` | `-5` | |
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Step-2: Pivot `=A_(2,2)=1`, 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)=(1 * -5 - -1 * 0)/(1)=-5` So matrix becomes | `A` | = | | `1` | `2` | `3` | | | `0` | `1` | `0` | | | `2` | `-1` | `-5` | |
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Determinant will be `A_(3,3)` multiplied by the scaling factor 1 `:.` Determinant `=-5` |
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