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Matrix multiplication

Rows times columns, entry by entry.

Entry (i, j) of AB is row i of A dotted with column j of B, which is why the inner dimensions must match. Every entry is computed in the open below. Matrix multiplication is composition of transformations, which is why it is not commutative.

Arbejdstxrd eksempel: [[1,2],[3,4]] * [[5,6],[7,8]]

Linear-Algebra · Matrix-Multiplication

[[1,2],[3,4]] * [[5,6],[7,8]]

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

Trin for trin

  1. \left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right] \left[\begin{matrix}5 & 6\\7 & 8\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)(5) + (2)(7) = 19

  3. c_{12} = (1)(6) + (2)(8) = 22

  4. c_{21} = (3)(5) + (4)(7) = 43

  5. c_{22} = (3)(6) + (4)(8) = 50

  6. AB = \left[\begin{matrix}19 & 22\\43 & 50\end{matrix}\right]

Afslør svaret
AB = \left[\begin{matrix}19 & 22\\43 & 50\end{matrix}\right]

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