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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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Determinant by gaussian elimination 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 Determinant by gaussian elimination ...
`[[2,1,3],[4,2,1],[1,3,2]]`Solution:Row echelon form Given matrix | | | `2` | `1` | `3` | | | `4` | `2` | `1` | | | `1` | `3` | `2` | |
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`R_2 larr R_2-2xx R_1` | = | | `2` | `1` | `3` | | | `0` | `0` | `-5` | | | `1` | `3` | `2` | |
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`R_3 larr R_3-0.5xx R_1` | = | | `2` | `1` | `3` | | | `0` | `0` | `-5` | | | `0` | `2.5` | `0.5` | |
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After interchanging rows `R_2 harr R_3`, Sign of determinant is changed | = - | | `2` | `1` | `3` | | | `0` | `2.5` | `0.5` | | | `0` | `0` | `-5` | |
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`=-(2*2.5*(-5))` `=25` |
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