Q1Single correct4 Marks6 Apr 2026

Let $T:\mathbb{R}^3\to\mathbb{R}^3$ be a linear transformation such that $T^2=T$, and $\operatorname{rank}(T)=2$. Which of the following statements is correct?

A

$T$ is the identity transformation.

B

$T$ maps every vector in $\mathbb{R}^3$ to a vector with at least one zero component.

C

$T$ is not injective.

D

$\operatorname{Im}(T)=\mathbb{R}^3$.