Let $A$ be an $n \times n$ real matrix for which two distinct non-zero $n$-dimensional real column vectors $v_{1}, v_{2}$ satisfy the relation $A v_{1}=A v_{2}$. Consider the following statements.
- At least one eigenvalue of $A$ is zero.
- $A$ is not full rank.
- Columns of $A$ are not linearly independent.
- $\operatorname{det}(A)=0$.
Which of the above statements is/are $\text{TRUE}?$
- Only $\text{(i)}$
- Only $\text{(ii)}$
- Only $\text{(iii)}$
- Only $\text{(iv)}$
- All of $\text{(i) – (iv)}$