/sci/ - Science & Math

Doing some true or false questions and I came across this one:
Why is this one false? I've been trying to wrap my head around it for a while. Assuming that the person doing the row operation did it perfectly and it results in an inconsistent system, wouldn't that just mean that the original system was inconsistent, to begin with because he couldn't find an answer?
The solution manual said false because:
1 0 | 1
0 1 | 0
0 0 | 0
but didn't say any more than just that.