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## Homework Statement

In class we learned some linear transformations where we have a stationary observer and another moving near the speed of light.

Describing the reference frames:

s' -> x'=u't'

s-> x=ut

Boundary conditions:

x=x'=t=t'=0

Therefore at the origin of x we have x=ut=0, x'=u't', x=-vt'

Using these for the transformations:

x'=Ax+Bt

t'=Cx+Dt

## Homework Equations

Final transforms:

[tex]x'=\gamma(x-vt)[/tex]

[tex]t'=\gamma(\frac{-vx}{c^2}+t)[/tex]

[tex]x=\gamma(x'+vt')[/tex]

[tex]t=\gamma(\frac{vx'}{c^2}+t')[/tex]

## The Attempt at a Solution

So I can solve these as long as I have my notes that I can follow so I know what to solve for and when. My professor ended up solving for the A,B,C,D first then subbing in gamma etc to arrive at the final results.

My questions is: I'd love to be able to derive these on my own. My problem I don't know what I am trying to solve for or the point of what I am solving for. Point may not be the best word - I understand the end result and know how it is used, I just don't understand the steps/method to get there. (the algebra I get, not the method.