Question: Let V be a vector space and assume that the maps f1, f2: V R1 are linear. (a) Define a map F: V R2 whose

Let V be a vector space and assume that the maps f1, f2: V †’ R1 are linear.
(a) Define a map F: V †’ R2 whose component functions are the given linear ones.

Show that F is linear.
(b) Does the converse hold-is any linear map from V to R2 made up of two linear component maps to R1?
(c) Generalize.

f2(v)

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