GATE EC 2025 Set 1 Q1 — Linear Algebra

Consider the matrix $A$ below:
$$A=\left[\begin{array}{llll} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{array}\right]$$

For which of the following combinations of $\alpha, \beta$, and $\gamma$, is the rank of $A$ at least three?

1. Only (i), (iii), and (iv)
2. Only (iv)
3. Only (ii)
4. Only (i) and (iii)