5-t should be 5+t

Thanks guys! I've made the corrections and added the details Bernhard asked. Let me know.

Thanks for adding this additional line. In the last step, when adding L2+L3 we would now get [0,0,t,-1], not [0,0,-1+t,-1], so that again the solutions needs to be adjusted! In fact, I would also like to see how you get back from the reduced matrix to the linear system to conclude consistency (x3 equation is enough).

Wow! I need to watch out that code a bit more closely. Thanks for your carful work!

I've corrected the solution and added the line you asked. (I also checked in wolfram alpha and the solution is now correct)