Q39Multiple correct2 Marks6 Aug 2023

Which of the following options are true?

A

There exists an onto linear transformation $T:\mathbb{R}^3\to\mathbb{R}^2$.

B

There does not exist a one-one linear transformation $T:\mathbb{R}^3\to\mathbb{R}$.

C

There exists a linear transformation $T:\mathbb{R}^3\to\mathbb{R}^2$ such that $\operatorname{rank}(T)=\operatorname{nullity}(T)$.

D

There does not exist a linear transformation $T:\mathbb{R}^2\to\mathbb{R}^3$ such that $\operatorname{rank}(T)=\operatorname{nullity}(T)$.