= Solution
Transforming the <electromagnetic field tensor> by $F'=\Lambda F\Lambda^T$ and reading off its components gives
$$
\boxed{
\begin{aligned}
&E_1'=E_1,
&&E_2'=\gamma(E_2-vB_3),
&&E_3'=\gamma(E_3+vB_2),\\
&B_1'=B_1,
&&B_2'=\gamma\left(B_2+\frac{vE_3}{c^2}\right),
&&B_3'=\gamma\left(B_3-\frac{vE_2}{c^2}\right).
\end{aligned}}
$$
These are the parallel and transverse <Lorentz transformation of electromagnetic fields>[field transformation laws] for a boost in the $x$ direction.
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