Matrix Determinant Calculator
Calculate the determinant of 2×2, 3×3, and 4×4 matrices. See the expansion steps using Sarrus' rule or Laplace cofactor expansion.
How to Use the Matrix Determinant Calculator
- Enter the numbers or values in the input fields.
- The result is calculated and displayed automatically.
- Review the step-by-step solution or detailed breakdown.
- Copy the result or adjust inputs for a new calculation.
مرجع سريع
| من | إلى |
|---|---|
| 2 + 3 | 5 |
| 12 × 12 | 144 |
| √144 | 12 |
| 2¹⁰ | 1,024 |
| π | 3.14159 |
| e | 2.71828 |
حالات الاستخدام
- •Checking homework or exam answers quickly and accurately.
- •Verifying manual calculations in professional or academic work.
- •Learning mathematical concepts with instant visual feedback.
- •Performing quick computations during meetings or presentations.
الصيغة
For a 2×2 matrix: det = ad − bc. For a 3×3 matrix, use cofactor expansion along the first row or Sarrus' rule. For a 4×4 matrix, use Laplace expansion: expand along the first row using 3×3 cofactors.
الأسئلة الشائعة
What is a matrix determinant?
The determinant is a scalar value computed from a square matrix. It indicates whether the matrix is invertible (det ≠ 0) or singular (det = 0), and represents the scaling factor of the linear transformation.
What is Sarrus' rule?
Sarrus' rule is a shortcut for computing 3×3 determinants. You sum the products of the three main diagonals and subtract the products of the three anti-diagonals.
What is Laplace expansion?
Laplace (cofactor) expansion computes a determinant by expanding along a row or column. Each element is multiplied by its cofactor (signed minor), and the results are summed.
When is a determinant zero?
A determinant is zero when the matrix is singular — its rows (or columns) are linearly dependent. This means the system of equations it represents has no unique solution.