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(3) Let V be a finite dimensional vector space, and let T: V® V be a...

(3) Let V be a finite dimensional vector space, and let T: V® V be a linear transformation such that rk(T) = rk(T2).

a) Show that ker(T) = ker(T2).

b) Show that 0 is the only vector that lies in both the null space of T, and the range space of T

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