# GATE Mechanical 2022 Set 2 | Question: 36

$A$ 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?

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