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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)

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