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$A$ is a $3 \times 5$ real matrix of rank $2$. For the set ot homogeneous equations $Ax = 0$, where $0$ is a zero vector and $x$ is a vector of unknown variables, which of the following is/are true?

- The given set of equations will have a unique solution.
- The given set of equations will be satisfied by a zero vector of appropriate size.
- The given set of equations will have infinitely many solutions.
- The given set of equations will have many but a finite number of solutions.