免费矩阵行列式计算器
计算2x2矩阵的行列式值。
Det
5.0000
公式
## 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 (-)
计算示例
Find the determinant of [[3, 7], [1, 4]].
- 01det = (3)(4) - (7)(1)
- 02= 12 - 7
- 03= 5
- 04Since det ≠ 0, the matrix is invertible
常见问题
What is the determinant?
The determinant is a scalar value computed from a square matrix. For 2×2 matrices, det = ad - bc. It indicates whether the matrix is invertible and the scaling factor of the transformation.
What does it mean when the determinant is zero?
A zero determinant means the matrix is singular (not invertible). The columns are linearly dependent, and the transformation collapses space.
How is the determinant used?
Determinants are used to solve systems of linear equations (Cramer's rule), find areas/volumes, check invertibility, and compute eigenvalues.
学习