3×3 Matrix Determinant
det = a(ei−fh) − b(di−fg) + c(dh−eg). Cofactor expansion.
Result
det(M)
1.000000
Invertible.
- Row 1[1, 2, 3]
- Row 2[0, 1, 4]
- Row 3[5, 6, 0]
- a(ei−fh)-24.0000
- −b(di−fg)40.0000
- +c(dh−eg)-15.0000
- Determinant1.000000
Step-by-step
- Cofactor expansion along row 1.
- det = a(ei−fh) − b(di−fg) + c(dh−eg) = 1.0000.
How to use this calculator
- Enter all 9 entries.
About this calculator
3×3 determinant via cofactor expansion: det = a(ei−fh) − b(di−fg) + c(dh−eg) for [[a,b,c],[d,e,f],[g,h,i]]. Geometric meaning: signed volume of parallelepiped spanned by rows. Determinant zero ⇒ matrix singular (rows linearly dependent). For larger matrices: row reduction or LU decomposition. Source: Wolfram MathWorld - Determinant.
Frequently asked
det = 0. No inverse. Rows linearly dependent. System Ax = b has 0 or ∞ solutions.
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