Question

Consider the following statements :
I. There exists a linear transformation from $\R^3$ to itself such that its range space and null space are the same.
II. There exists a linear transformation from $\R^2$ to itself such that its range space and null space are the same.
Then

• A. both I and II are TRUE
• B. I is TRUE but II is FALSE
• C. II is TRUE but I is FALSE
• D. both I and II are FALSE

Answer 1

Answer: (C)

II is TRUE but I is FALSE

Answer 2

The correct option is (C) : II is TRUE but I is FALSE.