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Linear-Algebra · Matrix-Multiplication

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

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

Step by step

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

    A 2×2 times a 2×1 gives a 2×1 matrix. Entry (i, j) is row i of A dotted with column j of B.

  2. c_{11} = (0)(1) + (-1)(0) = 0

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

  4. AB = \left[\begin{matrix}0\\1\end{matrix}\right]

Reveal the answer
AB = \left[\begin{matrix}0\\1\end{matrix}\right]