I am stuck on the following problem:
Let $T$ be arbitrary linear transformation from $\Bbb R^n$ to $\Bbb R^n$ which is not one-one.Then I have show that Rank $(T)=n-1.$
I know that Rank$(T)$+ Nullity $(T)=n \implies$ Rank$(T)=n-$Nullity$(T)$. But what is the Nullity of $T?$ Can someone point me in the right direction?
EDIT: It was in fact a multiple choice question where the options were :
1. Rank$(T)>0 \space $,
2. Rank$(T)<n \space$,
3.Rank$(T)=n \space$ ,
The answer was given to be option 4 (which appears to be wrong from the responses).So,choice 2 appears to be correct one.