GATE Mechanical 2022 Set 2 | Question: 36

Question

$A$ 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?

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