### Linear Operators : Finite dimensional Space and Nullity

Let V be a finite-dimensional real (i.e. F = R) vector space. Let T be an element of L(V)(set of operators on V), and assume that T^2 = 0. a) Prove that rangeT is contained in nullT. b) Prove that dimnullT >= (dimV )/2. Hint. Make use of a)