n×n Matrix Determinant Calculator
Compute the determinant of any n×n square matrix using Gaussian elimination with partial pivoting, and check whether the matrix is invertible.
Input
Enter one matrix row per line, separating numbers with spaces or commas. The matrix must be square (same number of rows and columns).
Result
Determinant (det A)
8
Size
3×3
Invertible
Yes
Input matrix
| 2 | 1 | 0 |
| 1 | 3 | 1 |
| 0 | 1 | 2 |
How it works
- Enter the matrix with one row per line, separating the numbers in each row with spaces or commas. Only square n×n matrices (equal number of rows and columns) can be evaluated.
- The determinant is computed with Gaussian elimination using partial pivoting (equivalent to LU decomposition). The largest-magnitude entry is chosen as the pivot for numerical stability, the matrix is reduced to upper-triangular form, and the product of the diagonal entries is taken and signed according to the number of row swaps.
- A non-zero determinant means the matrix is invertible (non-singular) and has an inverse. A determinant of zero means the matrix is singular and has no inverse.
- Because of floating-point arithmetic the result may carry tiny rounding errors. Values smaller than about 1e-9 in magnitude are shown as 0.
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n×n Matrix Determinant Calculator