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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.

Esempio di funzionamento: [[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]

Passo dopo passo

  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]

Rivela la risposta
AB = \left[\begin{matrix}19 & 22\\43 & 50\end{matrix}\right]

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Più in Linear Algebra

DeterminantsMatrix inverseEigenvalues and eigenvectorsRow reduction