Hello,

(a) Does there exist a linear map T : R^11-------->R^5 such that rank(T)=null(T)?

My attempt:Never because rank(T)+null(T)=dim(R^11)=11 , we obtain 2rank(T)=11, contradicting the fact that rank(T) is an integer.

(b) Does there exist a linear map T : R^6-------->R^2 such that 2rank(T) = nul(T)?

Yes. rank(T)+null(T)=dimm(R^6)=6

3rank(T)=6 so rank(T)=2

are these correct?

Thanks