Im a littlebit stuck here. Suppose $Ax=(1,1,1)$ doesn't have any solutions, but $Ax=(0,1,0)$ has one unique solution. How does this imply that $Ax=(0,0,0)$ has one uniqe solution?
I was thinking that if $b=(0,1,0)$, the augmented matrix $[A|b]~...~[R|c]$ where R is in RREF. Now if i replace any row of c with zero the system must still be consistent, and have a unique solution right? Do you guys have an easier explanation? Thanx :) (Algebra exam next week)
if $Ax=(1,1,1)$ doesn't have any solutions then $Ax=(0,0,0)$ has NOT one unique solution