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Linear-Algebra · Determinants

Det [[0,1,1],[1,0,1],[1,1,0]]

\left[\begin{matrix}0 & 1 & 1\\1 & 0 & 1\\1 & 1 & 0\end{matrix}\right]

Hatua kwa hatua

  1. \det\left[\begin{matrix}0 & 1 & 1\\1 & 0 & 1\\1 & 1 & 0\end{matrix}\right]

    Determinant of a 3×3 matrix.

  2. = + (0) \det\left[\begin{matrix}0 & 1\\1 & 0\end{matrix}\right] - (1) \det\left[\begin{matrix}1 & 1\\1 & 0\end{matrix}\right] + (1) \det\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]

    Cofactor (Laplace) expansion along the first row, with alternating signs + − +.

  3. = (0) + (1) + (1)

    Each 2×2 minor is ad − bc.

  4. \det A = 2

    Result.

Lafunua jibu
\det A = 2