Matrixdeterminante-Rechner

Berechnen Sie die Determinante einer 2×2-Matrix. Kostenloser Online-Matrixrechner.

a (row 1, col 1)

b (row 1, col 2)

c (row 2, col 1)

d (row 2, col 2)

Det

5.0000

Trace7.0000

Invertible1

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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 (-)

Lösungsbeispiel

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

Häufig Gestellte Fragen

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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