I know how to represent the cross product as the levi-civita symbol, but I don't know how to show it can be represented as the matrix equation
2026-04-23 14:31:07.1776954667
How to show the components of a force can be expressed in a matrix equation?
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$\mathbf{c} = \mathbf{a} \times \mathbf{b} = \begin{vmatrix} \mathbf{i} && \mathbf{j} && \mathbf{k} \\ a_x && a_y && a_z \\ b_x && b_y && b_z \end{vmatrix} = \begin{bmatrix} a_y b_z - a_z b_y \\ a_z b_x - a_x b_z \\ a_x b_y - a_y b_x \end{bmatrix}=\begin{bmatrix} 0 && - a_z && a_y \\ a_z && 0 && -a_x \\ -a_y && a_x && 0 \end{bmatrix} \begin{bmatrix} b_x \\ b_y \\ b_z \end{bmatrix} = \mathbf{Mb}$