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Linear-Algebra · Matrix-Multiplication

[[2,1,0],[1,2,0],[0,0,1]] * [[0],[0],[1]]

\left[\begin{matrix}2 & 1 & 0\\1 & 2 & 0\\0 & 0 & 1\end{matrix}\right] \left[\begin{matrix}0\\0\\1\end{matrix}\right]

Step by step

  1. \left[\begin{matrix}2 & 1 & 0\\1 & 2 & 0\\0 & 0 & 1\end{matrix}\right] \left[\begin{matrix}0\\0\\1\end{matrix}\right]

    A 3×3 times a 3×1 gives a 3×1 matrix. Entry (i, j) is row i of A dotted with column j of B.

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

  3. c_{21} = (1)(0) + (2)(0) + (0)(1) = 0

  4. c_{31} = (0)(0) + (0)(0) + (1)(1) = 1

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

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