Linear Algebra - explaining why system is singular.?

Question

This problem is asking me to explain why the system:

u + v + w = 2

u +2v +3w = 1

0 + v +2w = 0 is singular by finding a combination of the three equations that adds up to 0 = 1.

I'm not sure where to start, or what steps to do. I'm not really sure what singular means either. If you could help me understand or show me a good site that explains this clearly that would be a really big help. Thank you.

Answer 1

Singular means, "has no solution." Subtract the first equation from the second and then subtract the third from the result. You should get 0 =-1. Assuming there were a solution (u,v,w) this would imply 0=-1, which is absurd. Therefore there is no solution.