Consider the following statements:
I. There exists a linear transformation from ℝ3 to itself such that its range space and null space are the same.
II. There exists a linear transformation from ℝ2 to itself such that its range space and null space are the same.
Then ℝ2
1
both I and II are TRUE
2
I is TRUE but II is FALSE
3
II is TRUE but I is FALSE
4
both I and II are FALSE