 Solution

ID: past-exam-of-the-linear-algebra-course-of-the-university-of-oxford/2017/2/a/ii/solution

T^{'} : W^{'} ⟶ V^{'}, T^{'} (ϕ) = ϕ \circ T .

The composition is a linear functional on

V

, and pointwise operations give

T^{'} (a ϕ + b ψ) = a T^{'} ϕ + b T^{'} ψ

. Thus this really is a linear transformation; its direction reverses that of

T

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