# Let T: V- Wbe a linear transformation. Prove the following results. (a) N(T) = N(-T)

**Chapter 7, Problem 6**

(choose chapter or problem)

Let T: V- Wbe a linear transformation. Prove the following results. (a) N(T) = N(-T). (b) N(Tfc) = N((-T)fc). (c) If V = W (so that T is a linear operator on V) and A is an eigenvalue of T, then for any positive integer k N((T-Alv)fc ) = N((Al v -T)f c ).

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