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Linear-Algebra · Determinants

Det [[1,2,3],[4,5,6],[7,8,10]]

\left[\begin{matrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 10\end{matrix}\right]

Gawo ndi Gawo

  1. \det\left[\begin{matrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 10\end{matrix}\right]

    Determinant of a 3×3 matrix.

  2. = + (1) \det\left[\begin{matrix}5 & 6\\8 & 10\end{matrix}\right] - (2) \det\left[\begin{matrix}4 & 6\\7 & 10\end{matrix}\right] + (3) \det\left[\begin{matrix}4 & 5\\7 & 8\end{matrix}\right]

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

  3. = (2) + (4) + (-9)

    Each 2×2 minor is ad − bc.

  4. \det A = -3

    Result.

Kusonyeza yankho
\det A = -3