For an occurence, we can choose coordinates ct and x (calculating both time and space in length) ct and x thereby take on the form of a two dimensional vector.
Show that the same coordinates in S' are given by a matrice equation where the transformation matrix takes the form
$$\gamma \left( \begin{smallmatrix} 1&-\beta \\ -\beta&1 \end{smallmatrix} \right)$$
Where $\beta=\frac{v}{c}$
Is this really as simple as replacing t' for ct' in the definition: https://upload.wikimedia.org/math/e/3/e/e3ee37f49f0adb02bc81590cb697d4d0.png
It seems too simple?