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Determinants

2×2 by ad − bc, larger by cofactor expansion — and what the number means.

The determinant of a matrix is the factor by which it scales area (2×2) or volume (3×3), with a sign for orientation. A zero determinant means the matrix squashes space flat and cannot be inverted. The 3D view draws the column vectors and the box they span.

Exemplo trabalhado: det [[1,2],[3,4]]

Linear-Algebra · Determinants

Det [[1,2],[3,4]]

\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right]

Passo a passo

  1. \det\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right]

    Determinant of a 2×2 matrix.

  2. = (1)(4) - (2)(3)

    For 2×2: ad − bc.

  3. \det A = -2

    Result.

Revelar a resposta
\det A = -2

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