I'm trying to solve the following system of equations by matrix inversion, however when I substitute back my final solutions for x,y,z into the equations, one of them doesn't work. I checked everything a couple of times but I can't find the mistake.

Q: Solve the system of equations by matrix inversion if possible:

3x-2y+z=1

x+y+z=0

2x-y+2z=1

and here is the solution: ImageShack Album - 6 images

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