- #1
redyelloworange
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Homework Statement
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
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!