Linear Algebra
Matrix Determinant Calculator
Paste a square matrix and instantly obtain its determinant using Gaussian elimination.
Compute the determinant of a square matrix up to 6×6.
Determinant via LU decomposition
Row operations reduce the matrix to upper triangular form while tracking row swaps to assemble the determinant.
How to use
- Enter the matrix with each row on its own line.
- Separate entries with spaces or commas.
- Review the determinant and matrix order beneath the input.
Example
Input: 1 2 3\n0 4 5\n1 0 6
Output: det(A) = 22
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Matrix Determinant Calculator: matrix calculator, determinant calculator, matrix multiplication calculator, eigenvalue calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Matrix Determinant Calculator: Computes determinants for square matrices up to 6×6. It's built around determinant, matrix, linear algebra, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Row operations reduce the matrix to upper triangular form while tracking row swaps to assemble the determinant.
To use it well: (1) Enter the matrix with each row on its own line. (2) Separate entries with spaces or commas. (3) Review the determinant and matrix order beneath the input. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering 1 2 3\n0 4 5\n1 0 6 returns det(A) = 22. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
What size matrices are supported?
Any square matrix up to 6×6 for numerical stability. Larger matrices may suffer from floating-point rounding errors.
Can I detect singular matrices?
Yes—if the determinant is zero, the matrix is singular and does not have an inverse.
What formula does the Matrix Determinant Calculator use?
Row operations reduce the matrix to upper triangular form while tracking row swaps to assemble the determinant.
How do I use the Matrix Determinant Calculator?
Enter the matrix with each row on its own line. Separate entries with spaces or commas. Review the determinant and matrix order beneath the input.