Find the solution to linear transformations

Reference no: EM13124663

The solution to Linear transformations

Let L: V -- W be a linear transformation, and let T be a subspace of W. The inverse image of T denoted L^-1(T), is defined by L^-1(T) = {v e V | L(v) e T}. Show that L^-1(T) is a subspace of V.

A linear transformation L: V -- W is said to be one-to-one if L(v1) = L(v2) implies that v1=v2. Show that L is one-to-one if and only if ker(L) = {0v}.

Reference no: EM13124663

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