Linear Independence

April 6, 2008

Let V be a finite vector space over the set of rationals, and F be a linear transformation from V to V. Suppose x, y and z are vectors in V such that

(i) F(x) = y

(ii) F(y) = z

(iii) F(z) = x+y

Suppose x is nonzero. Show that x, y and z are linearly independent vectors.

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