Question: Let V be a vector space over F. A linear map P: V - V is called a projection if P = POP. (a) Let

Let V be a vector space over F. A linear map P: V - V is called a projection if P = POP. (a) Let T: R2 -> R2 defined by T(x, y) = (x,0). Show that T is a projection. (b) Let P: V - V be a projection. Prove that V = ker PO im P. (hint: for any U E V, consider U - P(U))

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