📊 Determinant of a Matrix Finder
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📌 Understanding Determinant of a Matrix
The determinant of a square matrix is a scalar value that provides useful properties about the matrix:
- It is only defined for square matrices (n × n).
- If the determinant is 0, the matrix is singular (non-invertible).
- For a 2×2 matrix: det(A) = ad – bc.
- For larger matrices, determinants are computed using row reduction or Laplace expansion.
📌 Example Calculations
| Matrix | Determinant |
|---|---|
| 1, 2; 3, 4 | -2 |
| 2, 5; 1, 3 | 1 |
| 3, 8, 4; 2, 6, 1; 5, 9, 7 | -15 |
🔧 Practical Applications of Matrix Determinants
1. Engineering & Physics: Used in solving systems of linear equations.
2. Computer Science: Helps in graphics transformations and cryptography.
3. Data Science: Important in statistical models and machine learning.
❓ FAQs
Q1: How do I calculate a determinant?
✅ Use row operations, Laplace expansion, or direct formulas for small matrices.
Q2: What happens if the determinant is 0?
✅ The matrix is singular and does not have an inverse.
Q3: Where is the determinant used?
✅ It is widely used in **mathematics, physics, and computer science**.
Q4: Can I enter non-square matrices?
⚠️ No, the determinant is only defined for square matrices.
Q5: How do I enter the matrix correctly?
✅ Enter rows separated by semicolons **(e.g., 1,2;3,4 for a 2×2 matrix)**.