(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let T:V W be a linear transformation. Prove the following results.

(a) N(T) = N(-T)

(b) N(T^k) = N((-T)^k)

(c) If V = W and t is an eigenvalue of T, then for any positive integer k

N((T-tI)^k) = N((tI-T)^k) where I is the identity transformation

3. The attempt at a solution

(a) for every x in V:

If T(x) = y, then –T(x) = -y

So then, T(0) = 0 = -T(0)

Is this right? On the right track?

I’m not sure how to approach the rest of them?

Thanks for your help!

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# Homework Help: Null spaces, transformations

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