Understanding Matrix Determinants

The determinant is a fundamental concept in linear algebra with applications in solving systems of equations, determining matrix invertibility, and understanding linear transformations.

How to Use This Calculator

Select your matrix size (2×2 to 6×6)
Enter values in the matrix cells (use decimal or fractions like 1/2)
Results compute automatically as you type
Use Random for example matrices or Clear to start over

Examples

2×2 Matrix: [[2, 1], [1, 2]] has determinant = 2×2 - 1×1 = 3

3×3 Matrix: [[1, 2, 3], [0, 1, 4], [5, 6, 0]] has determinant = 1

Properties of Determinants

Swapping rows changes sign
Scaling a row scales the determinant
Adding rows doesn't change value
Triangular matrix: product of diagonal
Zero determinant means matrix is singular

Frequently Asked Questions

What matrices are supported?

Square matrices from 2×2 to 6×6. Non-square matrices don't have determinants.

What precision is used?

Calculations use double-precision floating point (about 15 decimal digits). Results are rounded to 6 decimals for display.

Why is my determinant zero?

This indicates a singular matrix - either rows/columns are linearly dependent or the matrix contains all zeros.

What algorithm is used?

LU decomposition with partial pivoting for numerical stability, with fallback to Leibniz formula for very small matrices.

Determinant Calculator

Result

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Determinant Calculator - Fast Matrix Determinants

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