Q20Multiple correct3 Marks1 Dec 2024

Let $V=\operatorname{span}\{(3,0,0),(0,-2,2),(-1,1,-1)\}$. Let $T:V\to\mathbb{R}^2$ be defined by $T(x,y,z)=(cx-y,y+z)$. Choose all correct options.

A

$T$ is not one-one for any value of $c$.

B

$T$ is one-one when $c=0$.

C

$\operatorname{rank}(T)=1$ for all values of $c$.

D

$\operatorname{nullity}(T)=2$ for some $c$.

E

There exist non-zero real numbers $\alpha$ and $\beta$ such that $\alpha(3,0,0)+\beta(0,-2,2)\in\ker(T)$.