Question: Let V be a vector space and 7r : V > V a linear transformation such that 7r(7r(v)) = 7r(v) for all 1) E V.

Let V be a vector space and 7r : V > V a linear transformation such that 7r(7r(v)) = 7r(v) for all 1) E V. Show that if v is in both Ker(7r) and Image(7r), then V = 0V

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