FB1 Let F be a field, and for nZ>0 consider the F-vector space F3n with standard basis {ei1i3n}, where ei= (0,,0,1,0,,0) is the vector with 1 in the i th coordinate and Os everywhere else. Consider the linear map T:F3nF3n defined on the standard basis by ei{ei0ifi{1,,3n}isamultipleof3otherwise. What is the rank and the nullity of T