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\end{equation}  This matrix will become the covarient form of the electromagnetic tensor $F_{\mu\nu}$. However this is 6 equations for 8 unknowns, leaving two free parameters that could take any value in the input four-vectors $\textbf{r}_1,\textbf{r}_2$. But this shows that \begin{equation}  \textbf{E}={_t\textbf{r}_1} \times {_t\textbf{r}_2} \\  \end{equation}  That is the electric field corresponds to the corss product of the spatial comonents of the four vectors.