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Linear-Algebra · Matrix-Multiplication

[[1,1],[1,0]] * [[1,1],[1,0]]

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

Stap met stap

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

    A 2×2 times a 2×2 gives a 2×2 matrix. Entry (i, j) is row i of A dotted with column j of B.

  2. c_{11} = (1)(1) + (1)(1) = 2

  3. c_{12} = (1)(1) + (1)(0) = 1

  4. c_{21} = (1)(1) + (0)(1) = 1

  5. c_{22} = (1)(1) + (0)(0) = 1

  6. AB = \left[\begin{matrix}2 & 1\\1 & 1\end{matrix}\right]

Openbaar die antwoord
AB = \left[\begin{matrix}2 & 1\\1 & 1\end{matrix}\right]