Matrix Determinant Calculator
Calculate a square matrix determinant by pivoted elimination.
How the matrix determinant calculator works
A determinant summarizes whether a square matrix preserves independent dimensions and how it scales oriented area or volume. This calculator uses Gaussian elimination with partial pivoting, multiplying the resulting diagonal entries. Each row swap reverses the sign, and a missing usable pivot makes the determinant zero, signaling a singular matrix that has no inverse.
The default three-by-three matrix has rows 6, 1, 1; 4, minus 2, 5; and 2, 8, 7. Pivoted elimination and sign tracking produce the verified determinant minus 306. Because that value is nonzero, the columns are linearly independent and the same matrix is invertible.
Reading matrix determinant calculator results privately
Only square matrices have determinants, so unequal row and column counts are rejected. Pivoting improves numerical stability, but nearly singular decimal matrices can still yield a very small nonzero result affected by rounding. The displayed singular verdict uses a tolerance for that reason. Symbolic determinants and exact rational arithmetic are outside this numeric calculator. This matrix determinant calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
What does a zero determinant mean?
The rows or columns are linearly dependent. The matrix collapses at least one dimension and has no inverse.
Why does swapping rows change the sign?
A row swap reverses orientation, so each swap multiplies the determinant by minus one.
Is the matrix determinant calculator private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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