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Determinant Calculator
Find the determinant of 2x2 and 3x3 square matrices with a clear explanation of cofactor expansion and the Leibniz formula.
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Interactive Determinant Calculator Workspace
Matrix Determinant Resultdet(A) = -3
Determinant Expansion Steps
For a 2x2 matrix: det(A) = ad - bc
Identify coefficients: a = 1, b = 2, c = 4, d = 5
Diagonal terms: a × d = 1 × 5 = 5
Anti-diagonal terms: b × c = 2 × 4 = 8
Calculate: (5) - (8) = -3
Mathematical Formula & Variables
Equation Model
det(A) = ad - bc | det(3x3) = a(ei-fh) - b(di-fg) + c(dh-eg)For a 2x2 matrix, subtract the product of the antidiagonal from the product of the main diagonal. For a 3x3 matrix, use Laplace cofactor expansion along the top row.
Variable Definitions
| Symbol | Description |
|---|---|
| det(A) | The unique scalar value computed from a square matrix |
| a, b, c, ... | The individual numeric elements of the square matrix |
How to Use the Determinant Calculator
- Select matrix size (2x2 or 3x3).
- Input the numerical entries into the corresponding cells.
- Click calculate to output the determinant with direct step-by-step expansion terms.
Practical Example Calculation
Scenario Context: Calculating the determinant of a 2x2 matrix: A = [[3, 8], [4, 6]].
Step 1: Identify diagonal terms: a = 3, d = 6.
Step 2: Identify antidiagonal terms: b = 8, c = 4.
Step 3: Multiply main diagonal: 3 × 6 = 18.
Step 4: Multiply antidiagonal: 8 × 4 = 32.
Step 5: Subtract: 18 - 32 = -14.
The determinant det(A) is -14.
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