矩阵行列式计算器 — 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]].

    1. det = (3)(4) - (7)(1)
    2. = 12 - 7
    3. = 5
    4. Since det ≠ 0, the matrix is invertible