maths.free › Linear Algebra › Matrix multiplication

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.

Contoh yang dikerjakan: [[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]

Langkah demi langkah

  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]

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

Cubalah sendiri

Lebih dalam Linear Algebra

DeterminantsMatrix inverseEigenvalues and eigenvectorsRow reduction