How we worked it out
Updated as you change the numbers.
- Reduce A to triangular form by row operations (with partial pivoting); the determinant is the product of the diagonal, with the sign flipped for each row swap.
Method and assumptions
Determinants and inverses use Gaussian elimination with partial pivoting, which is accurate for well-conditioned matrices. Results are shown to six decimal places; tiny values from rounding are shown as 0.
Questions
When does a matrix have no inverse?
When its determinant is 0 (it is singular): its rows are not independent.
Sources
Method and figures checked on . Every worked answer on this page is covered by an automated test. Found a mistake? Tell us.