Matrix Determinant Calculator (2×2) — Formel
## 2×2 Matrix Determinant
### Formula
For matrix [[a, b], [c, d]]:
**det = ad - bc**
### Properties
- If det = 0, the matrix is **singular** (not invertible)
- If det ≠ 0, the matrix is **invertible**
- |det| gives the area scaling factor of the linear transformation
- sign of det indicates whether orientation is preserved (+) or reversed (-)
### Formula
For matrix [[a, b], [c, d]]:
**det = ad - bc**
### Properties
- If det = 0, the matrix is **singular** (not invertible)
- If det ≠ 0, the matrix is **invertible**
- |det| gives the area scaling factor of the linear transformation
- sign of det indicates whether orientation is preserved (+) or reversed (-)
Lösungsbeispiel
Find the determinant of [[3, 7], [1, 4]].
- det = (3)(4) - (7)(1)
- = 12 - 7
- = 5
- Since det ≠ 0, the matrix is invertible