Question

Let T:U→V be a linear transformation. Let 0_u and 0_v be zero vectors of U and V. Show that T(0_U )=0_V

Answer 1

Let U, V be a vector space

$O: V \implies$ to be a mapping such that o(v)= o_u where o_u is zero element in U

Now let $V_1, V_2 \epsilon V$

Then O(V₁+V₂) =0_u

$\implies T(0_U )=0_V$