Determinant Calculator
Calculate matrix determinants for 2x2, 3x3, and 4x4 matrices with step-by-step solutions
About the Determinant Calculator
The Determinant Calculator computes the determinant of square matrices up to 4x4. This essential linear algebra tool helps students and professionals solve systems of equations, find matrix inverses, and understand linear transformations.
Understanding determinants is fundamental in linear algebra and has applications across numerous fields including computer graphics, engineering, physics, and economics.
How to Use the Determinant Calculator
- Select the size of your matrix (2x2, 3x3, or 4x4)
- Enter the values for each element of the matrix
- Click "Calculate Determinant" to get the result
- View the step-by-step calculation process
Applications: Determinants are used in solving linear systems, finding matrix inverses, calculating areas and volumes, and in various engineering applications.
Determinant Properties
det = 0
Matrix is singular (non-invertible)
det ≠ 0
Matrix is invertible
|det|
Scaling factor of transformation
Determinant Formulas
2x2 Matrix:
det([a b; c d]) = ad - bc
3x3 Matrix (Rule of Sarrus):
det = a₁₁(a₂₂a₃₃ - a₂₃a₃₂) - a₁₂(a₂₁a₃₃ - a₂₃a₃₁) + a₁₃(a₂₁a₃₂ - a₂₂a₃₁)