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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.

ตัวอย่างที่ทำงานแล้ว: [[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]

ก้าวต่อก้าว

  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]

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

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