Let T be a linear transformation from V to V. Prove that T^2 = T0 (with T0 the zero mapping) IFF R(T) C N(T). ( "is contained in" = 'C'. )(adsbygoogle = window.adsbygoogle || []).push({});

Comments:

It seems clear that T is also the zero transformation. IF this is wrong can someone give me a counterexample. If it is true, then R(T) = { 0 } and N(T) = {v | v in V}, and clearly R(T) C N(T). That would show half, and if this part is right, then I can finish the second half. But is my reasoning for this part correct?--it almost seems too easy.

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# Proof help

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