 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-i/2/a/ii/solution

T : V \to W

between vector spaces over the same field

F

T (u + v) = T (u) + T (v), T (a v) = a T (v) (u, v \in V, a \in F) .

Equivalently,

T (a u + b v) = a T (u) + b T (v)

for all

u, v \in V

and

a, b \in F

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