Q1Single correct2 Marks3 Aug 2025

Let $A$ be a $3\times 5$ matrix whose row echelon form is $$\begin{bmatrix}1&2&-1&2&1\\0&0&1&3&-2\\0&0&0&k&0\end{bmatrix},$$ where $k\in\mathbb{R}$. Choose the correct option.

A

The nullity of $A$ is independent of the value of $k$.

B

The nullity of $A$ depends on $k$, and the set of all possible values for the nullity is $\{2\}$.

C

The nullity of $A$ depends on $k$, and the set of all possible values for the nullity is $\{0,1,2,3,4,5\}$.

D

The nullity of $A$ depends on $k$, and the set of all possible values for the nullity is $\{2,3\}$.