Question: Show that a linear function maps subspaces to subspaces, and vice versa. That is, if S is a subspace of X, then f (S) is

Show that a linear function maps subspaces to subspaces, and vice versa. That is, if S is a subspace of X, then f (S) is a subspace of Y; if T is a subspace of Y, then f-1(T) is a subspace of X.

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