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6 Nov 2019
Let V be a vector space. Let f : V rightarrow V be a bijection. Define two new operations + f and f as follows. If v and w are two vectors in V, v + f w is defined to be the vector f-l (f(v) + f(w)) where f-1 is the inverse function of f. If a is a scalar and v is a vector in V, a v is defined to be the vector f-1 (af(v)). Prove that V together with the new addition of vectors, +f, and the new multiplication of vectors by scalars, is also vector space. Show transcribed image text
Let V be a vector space. Let f : V rightarrow V be a bijection. Define two new operations + f and f as follows. If v and w are two vectors in V, v + f w is defined to be the vector f-l (f(v) + f(w)) where f-1 is the inverse function of f. If a is a scalar and v is a vector in V, a v is defined to be the vector f-1 (af(v)). Prove that V together with the new addition of vectors, +f, and the new multiplication of vectors by scalars, is also vector space.
Show transcribed image text