Suppose a linear transformation ( T: ℝⁿ → ℝⁿ ) has the property that ( T(u) = T(v) ) for some pair of distinct vectors ( u ) and ( v ) in ( ℝⁿ ). Can ( T ) map ( ℝⁿ ) onto ( ℝⁿ )? Why or why not?
a) Yes, because ( T ) is invertible
b) No, because ( T ) is not a one-to-one function
