# Cyclic Vector

Suppose that T is a linear operator on a two dimensional vector space V, and that T is not multiple of the identity transformation. Show that T has a cyclic vector (i.e., there exists v V such that {v, Tv } is a base for V).

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Suppose that T is a linear operator on a two dimensional vector space V, and that T is not multiple of the identity transformation. Show that T has a cyclic vector (i.e., there exists v V such that {v, ...

#### Solution Summary

A cyclic vector is proven. The solution is detailed and well presented.

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