🎓 Mathematics • Linear Algebra
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Determinant Calculator
Computes matrix determinant |A| for 2x2 and 3x3 matrices with expansion steps.
Dimensions:
Presets:
Matrix A (3 × 3)
Matrix B (3 × 3)
Matrix Product (A × B)
4
0
6
1
-5
6
16
18
7
What is a Matrix Determinant?
The determinant is a scalar value characterizing a square matrix.
Geometrically, it represents the scaling factor of area (in 2D) or volume (in 3D) under the linear transformation.
Formula & Step-by-Step Calculation
2x2: ad - bc, 3x3: a(ei - fh) - b(di - fg) + c(dh - eg)
Expansion by minors along the top row.
Worked Step-by-Step Examples
Example 1
det([[2, 3], [1, 4]])
Solution: 5
• (2 × 4) - (3 × 1) = 8 - 3 = 5
Common Real-World & Academic Use Cases
- ✓ Checking matrix invertibility
- ✓ Cramer’s Rule linear system solving
- ✓ Eigenvalue characteristic polynomial
How to Use the Determinant Calculator
1
Input Matrix Entries
Enter grid values.
2
Read Determinant
View scalar determinant value.
Frequently Asked Questions
Q: What if det(A) = 0?
The matrix is singular and cannot be inverted, mapping space onto a lower dimension.