Consider a linear homogeneous system of equations $\text{Ax}=0$, where $\text{A}$ is an $n \times n$ matrix, $\text{x}$ is an $n \times 1$ vector and $0$ is an $n \times 1$ null vector. Let $r$ be the rank of $\text{A}$. For a non-trivial solution to exist, which of the following conditions is/are satisfied?
- Determinant of $\text{A}=0$
- $r=n$
- $r < n$
- Determinant of $\text{A} \neq 0$