(adsbygoogle = window.adsbygoogle || []).push({}); Let T: V->V be a linear transformation where V is finite dimensional. Show ath exactly one of (i) an (ii) holds

i) T(v) = 0 for some v not zero in V

ii) T(x) = v has a solution x in V for every v in V

do they mean that if i holds then ii cannot hold?

Ok suppose i holds

T(v) = 0 for some v in V, v not zero

then T(T(v)) = T(0) = 0

let T(v) = x

then T(x) = 0

only solution here is x = v

So T(x) = 0 for all x. ANd thus is not possible for T(x) = v if T(v) = 0

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# Homework Help: Linear algebra proof

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