1. The problem statement, all variables and given/known data system of equations is as follows 4x +2y -2z = 0 2x + y -z= 1 3x +y -2z = 1 2. Relevant equations 3. The attempt at a solution Using gaussian elimination we can multiply mid-eq, by (-2) [[[actually... it is simply a basic equation procedure]]] 2x+y-z=1 |*(-2) = -4x -2y +2z = -2 further with using gaussian elimination (?) we sum together 4x+2y-2z=0 -4x-2y+2z=-2 result 0=-2 ´my teacher said something to the effect that, it is concluded that the system of equations does not have solutions... because a non-sensical result came out of the procedure. Now, my teacher gave me some kind of proof for the Gaussian elimination method, but I'm still little bit uncertain why the "untrue equation midresult" causes the entire system of eqiuation to not have solution... Our course ended today also, so I can't ask my teacher except by email. perhaps it's a dumb question but anyway... 1.) By what reasoning is it arrived to this conclusion that when a "non-sensical equation result" comes out from the procedure, that this "mid-result" if you allow me to call it that, causes the system of equations to not have solution (Therefore, you don't have to calculate any further using Gaussian elimination?) sorry if I failed to think about the problem rigorously enough as required by homework forum rules.