Calculadora de Determinante de Matriz

Calcule o determinante de uma matriz 2×2.

Det

5.0000

Trace7.0000
Invertible1
Ver formula →

Formula

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 (-)

    • Exemplo Resolvido

    Find the determinant of [[3, 7], [1, 4]].

    1. 01det = (3)(4) - (7)(1)
    2. 02= 12 - 7
    3. 03= 5
    4. 04Since det ≠ 0, the matrix is invertible

    Perguntas Frequentes

    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.

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