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Linear independence

A set of vectors is linearly independent if Ax=0 only has the trivial solution so Ax=b has a unique solution right?
But for this set of vectors (1,2,1,3)T (2,0,-1,2)T and (1,1,1,2)T when change it to row echelon form I get a row of zeros. Surely this means the system is inconsistent hence as there is no solutions for Ax=b, the set of vectors are linearly dependent...?

But the answers say this system is linearly independent :0

How can I show Ax=0 only has the trivial solution again?

Original post by Revengeissweet
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