Let $A $ be an $m \times n$ matrix of rank $n$ with real entries. Choose the correct statement.
1.$Ax=b$ has a solution for any $b$.
2.$Ax=0$ does not have a solution.
3.if $Ax=b$ has a solution then it is unique.
4.$y'A=0$ for some nonzero $y'$ where $y'$ is transpose of vector $y$
Now option 2 can be rejected because there is always $ x=0$.For option 3 if I take example \begin{bmatrix}1 \\ 2\end{bmatrix} and take $x _ (1\times 1) $ and taking $b$ aby vector then I get option 3 RIGHT. Am I right? And I want to know how to Answer it in more general way. Thanks very much in Advance