We normally assume that the origins of two inertial frames coincide at t=t'=0. This way we find:
t' = γ(t - vx/c2)
x' = γ(x-vt)
Suppose instead that when t=T the origin of S' (which is moving along the x-x' axis with speed v relative to S) has abscissa x=X (neglect y and z) and the S' clock at the origin of S' reads t'=0 at that moment.
a. How do the Lorentz transformations from S to S' need to be modified?
b. What about from S' to S?
c. Write these in matrix form.
Hint: you do not need to re-derive these transformations, try introducing an auxiliary frame that reduces the problem to the usual case.
Lorentz transformations (above)
The Attempt at a Solution
I don't know how to start this problem...