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Linear-Algebra · Matrix-Multiplication

[[1,0],[0,-1]] * [[3],[4]]

\left[\begin{matrix}1 & 0\\0 & -1\end{matrix}\right] \left[\begin{matrix}3\\4\end{matrix}\right]

Step by step

  1. \left[\begin{matrix}1 & 0\\0 & -1\end{matrix}\right] \left[\begin{matrix}3\\4\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} = (1)(3) + (0)(4) = 3

  3. c_{21} = (0)(3) + (-1)(4) = -4

  4. AB = \left[\begin{matrix}3\\-4\end{matrix}\right]

Reveal the answer
AB = \left[\begin{matrix}3\\-4\end{matrix}\right]