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Linear-Algebra · Matrix-Inverse

Inverse of [[3,6],[6,14]]

\left[\begin{matrix}3 & 6\\6 & 14\end{matrix}\right]

Steg för steg

  1. \det A = 6

    A matrix is invertible only when its determinant is non-zero.

  2. A^{-1} = \frac{1}{\det A}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix} = \frac{1}{6}\left[\begin{matrix}14 & -6\\-6 & 3\end{matrix}\right]

    For 2×2: swap the diagonal, negate the off-diagonal, divide by the determinant.

  3. A^{-1} = \left[\begin{matrix}\frac{7}{3} & -1\\-1 & \frac{1}{2}\end{matrix}\right]

Avslöja svaret
A^{-1} = \left[\begin{matrix}\frac{7}{3} & -1\\-1 & \frac{1}{2}\end{matrix}\right]