Q36Multiple correct2 Marks3 Dec 2023

Let $T$ be a linear transformation from $\mathbb{R}^2$ to $\mathbb{R}^3$. Let $S\subset\mathbb{R}^2$ be a line passing through the origin. Which of the following are possible?

A

$T(S)$ could be the origin in $\mathbb{R}^3$.

B

$T(S)$ could be a line passing through the origin in $\mathbb{R}^3$.

C

$T(S)$ could be a plane passing through the origin in $\mathbb{R}^3$.

D

$T(S)$ could be $\mathbb{R}^3$.