Exercise 12

After Theorem 1.5 we note that multiplying a row by $0$ is not allowed because that could change a solution set. Give an example of a system with solution set $S_{0}$ where after multiplying a row by $0$ the new system has a solution set $S_{1}$ and $S_{0}$ is a proper subset of $S_{1}$, that is, $S_{0}\neq S_{1}$. Give an example where $S_{0}=S_{1}$.